E
Identifieur interne : 001A88 ( Istex/Corpus ); précédent : 001A87; suivant : 001A89E
Auteurs : V. M. Tikhomirov ; S. A. Stepanov ; A. B. Ivanov ; L. V. Kantorovich ; E. B. Ershov ; M. I. Vo Tsekhovski ; V. G. Ushakov ; Ya. Yu. Nikitin ; M. S. Nikulin ; L. D. Kudryavtsev ; V. S. Shul An ; N. V. Butenin ; T. S. Pigolkina ; V. G. Prikazchikov ; A. B. Bakushinski ; V. M. Babich ; Yu. B. Rudyak ; D. D. Sokolov ; L. P. Kuptsov ; I. A. Kvasnikov ; I. N. Vekua ; R. A. Kordzadze ; Yu. N. Subbotin ; O. A. Ivanova ; V. N. Grishin ; D. A. Suprunenko ; A. V. Prokhorov ; B. A. Sevast Anov ; A. A. Bukhshtab ; V. I. Nechaev ; Yu. L. Ershov ; M. A. Ta Tslin ; E. B. Vinberg ; E. D. Solomentsev ; Yu. G. Zarkhin ; Val. S. Kulikov ; M. A. Shubin ; V. B. Andreev ; N. Kh. Rozov ; M. Sh. Tsalenko ; L. V. Kuz In ; L. M. Gluskin ; Yu. A. Bakhturin ; N. N. Vil Ams ; V. V. Gorbatsevich ; A. F. Leont V ; E. P. Dolzhenko ; R. L. Dobrushin ; V. V. Prelov ; D. V. Anosov ; V. E. Plisko ; N. M. Nagorny ; S. S. Goncharov ; I. A. Lavrov ; V. M. Mikheev ; V. A. Zalgaller ; M. V. Fedoryuk ; V. G. Boltyanski ; Ü. Lamiste ; L. A. Sidorov ; E. M. Semenov ; V. P. Petrenko ; S. N. Artemov ; A. I. Shtern ; I. I. Volkov ; Yu. I. Yanov ; E. G. Sklyarenko ; B. M. Bredikhin ; P. S. Soltan ; A. M. Stepin ; A. V. Prokhov ; G. D. Kim ; V. M. Sidel Ikov ; L. N. Bol Hev ; A. L. Semenov ; V. I. Danilov ; Ü. Lumiste ; V. L. Popov ; S. M. Voronin ; S. V. Matveev ; A. F. Kharshiladze ; I. B. Vapnyarski ; I. Kh. Sabitov ; P. S. Modenov ; Yu. A. Brychkov ; A. P. Prudnikov ; M. K. Samarin ; A. A. Mal Sev ; A. D. Myshkis ; V. E. Govorov ; A. L. Onishchik ; V. A. Iskovskikh ; M. G. Shur ; V. A. Sevast Anov ; A. S. Fedenko ; B. A. Efimov ; A. V. Mikhalev ; E. V. Pankrat V ; A. K. Tolpygo ; A. I. Loginov ; D. A. Ponomarev ; E. V. Shikin ; L. D. Kydryavtsev ; G. V. Kuz Ina ; F. P. Vasil V ; A. V. Arkhangel KiSource :
- Encyclopaedia of Mathematics ; 1995.
Abstract
Abstract: ϵ-ENTROPY of a set in a metric space - The logarithm to the base 2 of the smallest number of points in an ϵ-net for this set. In other words, the ϵ-entropy ℋϵ(C, X) of a set C lying in a metric space (X, ρ)
Url:
DOI: 10.1007/978-1-4899-3795-7_3
Links to Exploration step
ISTEX:8317721E19D38B916369B37018914CFCDFF37060Le document en format XML
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Pigolkina</name></author><author><name sortKey="Prikazchikov, V G" sort="Prikazchikov, V G" uniqKey="Prikazchikov V" first="V. G." last="Prikazchikov">V. G. Prikazchikov</name></author><author><name sortKey="Bakushinski, A B" sort="Bakushinski, A B" uniqKey="Bakushinski A" first="A. B." last="Bakushinski">A. B. Bakushinski</name></author><author><name sortKey="Babich, V M" sort="Babich, V M" uniqKey="Babich V" first="V. M." last="Babich">V. M. Babich</name></author><author><name sortKey="Rudyak, Yu B" sort="Rudyak, Yu B" uniqKey="Rudyak Y" first="Yu. B." last="Rudyak">Yu. B. Rudyak</name></author><author><name sortKey="Sokolov, D D" sort="Sokolov, D D" uniqKey="Sokolov D" first="D. D." last="Sokolov">D. D. Sokolov</name></author><author><name sortKey="Kuptsov, L P" sort="Kuptsov, L P" uniqKey="Kuptsov L" first="L. P." last="Kuptsov">L. P. Kuptsov</name></author><author><name sortKey="Kvasnikov, I A" sort="Kvasnikov, I A" uniqKey="Kvasnikov I" first="I. A." last="Kvasnikov">I. A. 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Sabitov</name></author><author><name sortKey="Modenov, P S" sort="Modenov, P S" uniqKey="Modenov P" first="P. S." last="Modenov">P. S. Modenov</name></author><author><name sortKey="Brychkov, Yu A" sort="Brychkov, Yu A" uniqKey="Brychkov Y" first="Yu. A." last="Brychkov">Yu. A. Brychkov</name></author><author><name sortKey="Prudnikov, A P" sort="Prudnikov, A P" uniqKey="Prudnikov A" first="A. P." last="Prudnikov">A. P. Prudnikov</name></author><author><name sortKey="Samarin, M K" sort="Samarin, M K" uniqKey="Samarin M" first="M. K." last="Samarin">M. K. Samarin</name></author><author><name sortKey="Mal Sev, A A" sort="Mal Sev, A A" uniqKey="Mal Sev A" first="A. A." last="Mal Sev">A. A. Mal Sev</name></author><author><name sortKey="Myshkis, A D" sort="Myshkis, A D" uniqKey="Myshkis A" first="A. D." last="Myshkis">A. D. Myshkis</name></author><author><name sortKey="Govorov, V E" sort="Govorov, V E" uniqKey="Govorov V" first="V. E." last="Govorov">V. E. Govorov</name></author><author><name sortKey="Onishchik, A L" sort="Onishchik, A L" uniqKey="Onishchik A" first="A. L." last="Onishchik">A. L. Onishchik</name></author><author><name sortKey="Iskovskikh, V A" sort="Iskovskikh, V A" uniqKey="Iskovskikh V" first="V. A." last="Iskovskikh">V. A. Iskovskikh</name></author><author><name sortKey="Shur, M G" sort="Shur, M G" uniqKey="Shur M" first="M. G." last="Shur">M. G. Shur</name></author><author><name sortKey="Sevast Anov, V A" sort="Sevast Anov, V A" uniqKey="Sevast Anov V" first="V. A." last="Sevast Anov">V. A. Sevast Anov</name></author><author><name sortKey="Fedenko, A S" sort="Fedenko, A S" uniqKey="Fedenko A" first="A. S." last="Fedenko">A. S. Fedenko</name></author><author><name sortKey="Efimov, B A" sort="Efimov, B A" uniqKey="Efimov B" first="B. A." last="Efimov">B. A. Efimov</name></author><author><name sortKey="Mikhalev, A V" sort="Mikhalev, A V" uniqKey="Mikhalev A" first="A. V." last="Mikhalev">A. V. Mikhalev</name></author><author><name sortKey="Pankrat V, E V" sort="Pankrat V, E V" uniqKey="Pankrat V E" first="E. V." last="Pankrat V">E. V. Pankrat V</name></author><author><name sortKey="Tolpygo, A K" sort="Tolpygo, A K" uniqKey="Tolpygo A" first="A. K." last="Tolpygo">A. K. Tolpygo</name></author><author><name sortKey="Loginov, A I" sort="Loginov, A I" uniqKey="Loginov A" first="A. I." last="Loginov">A. I. Loginov</name></author><author><name sortKey="Ponomarev, D A" sort="Ponomarev, D A" uniqKey="Ponomarev D" first="D. A." last="Ponomarev">D. A. Ponomarev</name></author><author><name sortKey="Shikin, E V" sort="Shikin, E V" uniqKey="Shikin E" first="E. V." last="Shikin">E. V. Shikin</name></author><author><name sortKey="Kydryavtsev, L D" sort="Kydryavtsev, L D" uniqKey="Kydryavtsev L" first="L. D." last="Kydryavtsev">L. D. Kydryavtsev</name></author><author><name sortKey="Kuz Ina, G V" sort="Kuz Ina, G V" uniqKey="Kuz Ina G" first="G. V." last="Kuz Ina">G. V. Kuz Ina</name></author><author><name sortKey="Vasil V, F P" sort="Vasil V, F P" uniqKey="Vasil V F" first="F. P." last="Vasil V">F. P. Vasil V</name></author><author><name sortKey="Arkhangel Ki, A V" sort="Arkhangel Ki, A V" uniqKey="Arkhangel Ki A" first="A. V." last="Arkhangel Ki">A. V. Arkhangel Ki</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:8317721E19D38B916369B37018914CFCDFF37060</idno><date when="1995" year="1995">1995</date><idno type="doi">10.1007/978-1-4899-3795-7_3</idno><idno type="url">https://api.istex.fr/document/8317721E19D38B916369B37018914CFCDFF37060/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001A88</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001A88</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">E</title><author><name sortKey="Tikhomirov, V M" sort="Tikhomirov, V M" uniqKey="Tikhomirov V" first="V. M." last="Tikhomirov">V. M. Tikhomirov</name></author><author><name sortKey="Stepanov, S A" sort="Stepanov, S A" uniqKey="Stepanov S" first="S. A." last="Stepanov">S. A. Stepanov</name></author><author><name sortKey="Ivanov, A B" sort="Ivanov, A B" uniqKey="Ivanov A" first="A. B." last="Ivanov">A. B. Ivanov</name></author><author><name sortKey="Kantorovich, L V" sort="Kantorovich, L V" uniqKey="Kantorovich L" first="L. V." last="Kantorovich">L. V. Kantorovich</name></author><author><name sortKey="Ershov, E B" sort="Ershov, E B" uniqKey="Ershov E" first="E. B." last="Ershov">E. B. Ershov</name></author><author><name sortKey="Vo Tsekhovski, M I" sort="Vo Tsekhovski, M I" uniqKey="Vo Tsekhovski M" first="M. I." last="Vo Tsekhovski">M. I. Vo Tsekhovski</name></author><author><name sortKey="Ushakov, V G" sort="Ushakov, V G" uniqKey="Ushakov V" first="V. G." last="Ushakov">V. G. Ushakov</name></author><author><name sortKey="Nikitin, Ya Yu" sort="Nikitin, Ya Yu" uniqKey="Nikitin Y" first="Ya. Yu." last="Nikitin">Ya. Yu. Nikitin</name></author><author><name sortKey="Nikulin, M S" sort="Nikulin, M S" uniqKey="Nikulin M" first="M. S." last="Nikulin">M. S. Nikulin</name></author><author><name sortKey="Kudryavtsev, L D" sort="Kudryavtsev, L D" uniqKey="Kudryavtsev L" first="L. D." last="Kudryavtsev">L. D. Kudryavtsev</name></author><author><name sortKey="Shul An, V S" sort="Shul An, V S" uniqKey="Shul An V" first="V. S." last="Shul An">V. S. Shul An</name></author><author><name sortKey="Butenin, N V" sort="Butenin, N V" uniqKey="Butenin N" first="N. V." last="Butenin">N. V. Butenin</name></author><author><name sortKey="Pigolkina, T S" sort="Pigolkina, T S" uniqKey="Pigolkina T" first="T. S." last="Pigolkina">T. S. Pigolkina</name></author><author><name sortKey="Prikazchikov, V G" sort="Prikazchikov, V G" uniqKey="Prikazchikov V" first="V. G." last="Prikazchikov">V. G. Prikazchikov</name></author><author><name sortKey="Bakushinski, A B" sort="Bakushinski, A B" uniqKey="Bakushinski A" first="A. B." last="Bakushinski">A. B. Bakushinski</name></author><author><name sortKey="Babich, V M" sort="Babich, V M" uniqKey="Babich V" first="V. M." last="Babich">V. M. Babich</name></author><author><name sortKey="Rudyak, Yu B" sort="Rudyak, Yu B" uniqKey="Rudyak Y" first="Yu. B." last="Rudyak">Yu. B. Rudyak</name></author><author><name sortKey="Sokolov, D D" sort="Sokolov, D D" uniqKey="Sokolov D" first="D. D." last="Sokolov">D. D. Sokolov</name></author><author><name sortKey="Kuptsov, L P" sort="Kuptsov, L P" uniqKey="Kuptsov L" first="L. P." last="Kuptsov">L. P. Kuptsov</name></author><author><name sortKey="Kvasnikov, I A" sort="Kvasnikov, I A" uniqKey="Kvasnikov I" first="I. A." last="Kvasnikov">I. A. Kvasnikov</name></author><author><name sortKey="Vekua, I N" sort="Vekua, I N" uniqKey="Vekua I" first="I. N." last="Vekua">I. N. Vekua</name></author><author><name sortKey="Kordzadze, R A" sort="Kordzadze, R A" uniqKey="Kordzadze R" first="R. A." last="Kordzadze">R. A. Kordzadze</name></author><author><name sortKey="Subbotin, Yu N" sort="Subbotin, Yu N" uniqKey="Subbotin Y" first="Yu. N." last="Subbotin">Yu. N. Subbotin</name></author><author><name sortKey="Ivanova, O A" sort="Ivanova, O A" uniqKey="Ivanova O" first="O. A." last="Ivanova">O. A. Ivanova</name></author><author><name sortKey="Grishin, V N" sort="Grishin, V N" uniqKey="Grishin V" first="V. N." last="Grishin">V. N. Grishin</name></author><author><name sortKey="Suprunenko, D A" sort="Suprunenko, D A" uniqKey="Suprunenko D" first="D. A." last="Suprunenko">D. A. Suprunenko</name></author><author><name sortKey="Prokhorov, A V" sort="Prokhorov, A V" uniqKey="Prokhorov A" first="A. V." last="Prokhorov">A. V. Prokhorov</name></author><author><name sortKey="Sevast Anov, B A" sort="Sevast Anov, B A" uniqKey="Sevast Anov B" first="B. A." last="Sevast Anov">B. A. Sevast Anov</name></author><author><name sortKey="Bukhshtab, A A" sort="Bukhshtab, A A" uniqKey="Bukhshtab A" first="A. A." last="Bukhshtab">A. A. Bukhshtab</name></author><author><name sortKey="Nechaev, V I" sort="Nechaev, V I" uniqKey="Nechaev V" first="V. I." last="Nechaev">V. I. Nechaev</name></author><author><name sortKey="Ershov, Yu L" sort="Ershov, Yu L" uniqKey="Ershov Y" first="Yu. L." last="Ershov">Yu. L. Ershov</name></author><author><name sortKey="Ta Tslin, M A" sort="Ta Tslin, M A" uniqKey="Ta Tslin M" first="M. A." last="Ta Tslin">M. A. Ta Tslin</name></author><author><name sortKey="Vinberg, E B" sort="Vinberg, E B" uniqKey="Vinberg E" first="E. B." last="Vinberg">E. B. Vinberg</name></author><author><name sortKey="Solomentsev, E D" sort="Solomentsev, E D" uniqKey="Solomentsev E" first="E. D." last="Solomentsev">E. D. Solomentsev</name></author><author><name sortKey="Zarkhin, Yu G" sort="Zarkhin, Yu G" uniqKey="Zarkhin Y" first="Yu. G." last="Zarkhin">Yu. G. Zarkhin</name></author><author><name sortKey="Kulikov, Val S" sort="Kulikov, Val S" uniqKey="Kulikov V" first="Val. S." last="Kulikov">Val. S. Kulikov</name></author><author><name sortKey="Shubin, M A" sort="Shubin, M A" uniqKey="Shubin M" first="M. A." last="Shubin">M. A. Shubin</name></author><author><name sortKey="Andreev, V B" sort="Andreev, V B" uniqKey="Andreev V" first="V. B." last="Andreev">V. B. Andreev</name></author><author><name sortKey="Rozov, N Kh" sort="Rozov, N Kh" uniqKey="Rozov N" first="N. Kh." last="Rozov">N. Kh. Rozov</name></author><author><name sortKey="Tsalenko, M Sh" sort="Tsalenko, M Sh" uniqKey="Tsalenko M" first="M. Sh." last="Tsalenko">M. Sh. Tsalenko</name></author><author><name sortKey="Kuz In, L V" sort="Kuz In, L V" uniqKey="Kuz In L" first="L. V." last="Kuz In">L. V. Kuz In</name></author><author><name sortKey="Gluskin, L M" sort="Gluskin, L M" uniqKey="Gluskin L" first="L. M." last="Gluskin">L. M. Gluskin</name></author><author><name sortKey="Bakhturin, Yu A" sort="Bakhturin, Yu A" uniqKey="Bakhturin Y" first="Yu. A." last="Bakhturin">Yu. A. Bakhturin</name></author><author><name sortKey="Vil Ams, N N" sort="Vil Ams, N N" uniqKey="Vil Ams N" first="N. N." last="Vil Ams">N. N. Vil Ams</name></author><author><name sortKey="Gorbatsevich, V V" sort="Gorbatsevich, V V" uniqKey="Gorbatsevich V" first="V. V." last="Gorbatsevich">V. V. Gorbatsevich</name></author><author><name sortKey="Leont V, A F" sort="Leont V, A F" uniqKey="Leont V A" first="A. F." last="Leont V">A. F. Leont V</name></author><author><name sortKey="Dolzhenko, E P" sort="Dolzhenko, E P" uniqKey="Dolzhenko E" first="E. P." last="Dolzhenko">E. P. Dolzhenko</name></author><author><name sortKey="Dobrushin, R L" sort="Dobrushin, R L" uniqKey="Dobrushin R" first="R. L." last="Dobrushin">R. L. Dobrushin</name></author><author><name sortKey="Prelov, V V" sort="Prelov, V V" uniqKey="Prelov V" first="V. V." last="Prelov">V. V. Prelov</name></author><author><name sortKey="Anosov, D V" sort="Anosov, D V" uniqKey="Anosov D" first="D. V." last="Anosov">D. V. Anosov</name></author><author><name sortKey="Plisko, V E" sort="Plisko, V E" uniqKey="Plisko V" first="V. E." last="Plisko">V. E. Plisko</name></author><author><name sortKey="Nagorny, N M" sort="Nagorny, N M" uniqKey="Nagorny N" first="N. M." last="Nagorny">N. M. Nagorny</name></author><author><name sortKey="Goncharov, S S" sort="Goncharov, S S" uniqKey="Goncharov S" first="S. S." last="Goncharov">S. S. Goncharov</name></author><author><name sortKey="Lavrov, I A" sort="Lavrov, I A" uniqKey="Lavrov I" first="I. A." last="Lavrov">I. A. Lavrov</name></author><author><name sortKey="Mikheev, V M" sort="Mikheev, V M" uniqKey="Mikheev V" first="V. M." last="Mikheev">V. M. Mikheev</name></author><author><name sortKey="Zalgaller, V A" sort="Zalgaller, V A" uniqKey="Zalgaller V" first="V. A." last="Zalgaller">V. A. Zalgaller</name></author><author><name sortKey="Fedoryuk, M V" sort="Fedoryuk, M V" uniqKey="Fedoryuk M" first="M. V." last="Fedoryuk">M. V. Fedoryuk</name></author><author><name sortKey="Boltyanski, V G" sort="Boltyanski, V G" uniqKey="Boltyanski V" first="V. G." last="Boltyanski">V. G. Boltyanski</name></author><author><name sortKey="Lamiste, U" sort="Lamiste, U" uniqKey="Lamiste U" first="Ü." last="Lamiste">Ü. Lamiste</name></author><author><name sortKey="Sidorov, L A" sort="Sidorov, L A" uniqKey="Sidorov L" first="L. A." last="Sidorov">L. A. Sidorov</name></author><author><name sortKey="Semenov, E M" sort="Semenov, E M" uniqKey="Semenov E" first="E. M." last="Semenov">E. M. Semenov</name></author><author><name sortKey="Petrenko, V P" sort="Petrenko, V P" uniqKey="Petrenko V" first="V. P." last="Petrenko">V. P. Petrenko</name></author><author><name sortKey="Artemov, S N" sort="Artemov, S N" uniqKey="Artemov S" first="S. N." last="Artemov">S. N. Artemov</name></author><author><name sortKey="Shtern, A I" sort="Shtern, A I" uniqKey="Shtern A" first="A. I." last="Shtern">A. I. Shtern</name></author><author><name sortKey="Volkov, I I" sort="Volkov, I I" uniqKey="Volkov I" first="I. I." last="Volkov">I. I. Volkov</name></author><author><name sortKey="Yanov, Yu I" sort="Yanov, Yu I" uniqKey="Yanov Y" first="Yu. I." last="Yanov">Yu. I. Yanov</name></author><author><name sortKey="Sklyarenko, E G" sort="Sklyarenko, E G" uniqKey="Sklyarenko E" first="E. G." last="Sklyarenko">E. G. Sklyarenko</name></author><author><name sortKey="Bredikhin, B M" sort="Bredikhin, B M" uniqKey="Bredikhin B" first="B. M." last="Bredikhin">B. M. Bredikhin</name></author><author><name sortKey="Soltan, P S" sort="Soltan, P S" uniqKey="Soltan P" first="P. S." last="Soltan">P. S. Soltan</name></author><author><name sortKey="Stepin, A M" sort="Stepin, A M" uniqKey="Stepin A" first="A. M." last="Stepin">A. M. Stepin</name></author><author><name sortKey="Prokhov, A V" sort="Prokhov, A V" uniqKey="Prokhov A" first="A. V." last="Prokhov">A. V. Prokhov</name></author><author><name sortKey="Kim, G D" sort="Kim, G D" uniqKey="Kim G" first="G. D." last="Kim">G. D. Kim</name></author><author><name sortKey="Sidel Ikov, V M" sort="Sidel Ikov, V M" uniqKey="Sidel Ikov V" first="V. M." last="Sidel Ikov">V. M. Sidel Ikov</name></author><author><name sortKey="Bol Hev, L N" sort="Bol Hev, L N" uniqKey="Bol Hev L" first="L. N." last="Bol Hev">L. N. Bol Hev</name></author><author><name sortKey="Semenov, A L" sort="Semenov, A L" uniqKey="Semenov A" first="A. L." last="Semenov">A. L. Semenov</name></author><author><name sortKey="Danilov, V I" sort="Danilov, V I" uniqKey="Danilov V" first="V. I." last="Danilov">V. I. Danilov</name></author><author><name sortKey="Lumiste, U" sort="Lumiste, U" uniqKey="Lumiste U" first="Ü." last="Lumiste">Ü. Lumiste</name></author><author><name sortKey="Popov, V L" sort="Popov, V L" uniqKey="Popov V" first="V. L." last="Popov">V. L. Popov</name></author><author><name sortKey="Voronin, S M" sort="Voronin, S M" uniqKey="Voronin S" first="S. M." last="Voronin">S. M. Voronin</name></author><author><name sortKey="Matveev, S V" sort="Matveev, S V" uniqKey="Matveev S" first="S. V." last="Matveev">S. V. Matveev</name></author><author><name sortKey="Kharshiladze, A F" sort="Kharshiladze, A F" uniqKey="Kharshiladze A" first="A. F." last="Kharshiladze">A. F. Kharshiladze</name></author><author><name sortKey="Vapnyarski, I B" sort="Vapnyarski, I B" uniqKey="Vapnyarski I" first="I. B." last="Vapnyarski">I. B. Vapnyarski</name></author><author><name sortKey="Sabitov, I Kh" sort="Sabitov, I Kh" uniqKey="Sabitov I" first="I. Kh." last="Sabitov">I. Kh. Sabitov</name></author><author><name sortKey="Modenov, P S" sort="Modenov, P S" uniqKey="Modenov P" first="P. S." last="Modenov">P. S. Modenov</name></author><author><name sortKey="Brychkov, Yu A" sort="Brychkov, Yu A" uniqKey="Brychkov Y" first="Yu. A." last="Brychkov">Yu. A. Brychkov</name></author><author><name sortKey="Prudnikov, A P" sort="Prudnikov, A P" uniqKey="Prudnikov A" first="A. P." last="Prudnikov">A. P. Prudnikov</name></author><author><name sortKey="Samarin, M K" sort="Samarin, M K" uniqKey="Samarin M" first="M. K." last="Samarin">M. K. Samarin</name></author><author><name sortKey="Mal Sev, A A" sort="Mal Sev, A A" uniqKey="Mal Sev A" first="A. A." last="Mal Sev">A. A. Mal Sev</name></author><author><name sortKey="Myshkis, A D" sort="Myshkis, A D" uniqKey="Myshkis A" first="A. D." last="Myshkis">A. D. Myshkis</name></author><author><name sortKey="Govorov, V E" sort="Govorov, V E" uniqKey="Govorov V" first="V. E." last="Govorov">V. E. Govorov</name></author><author><name sortKey="Onishchik, A L" sort="Onishchik, A L" uniqKey="Onishchik A" first="A. L." last="Onishchik">A. L. Onishchik</name></author><author><name sortKey="Iskovskikh, V A" sort="Iskovskikh, V A" uniqKey="Iskovskikh V" first="V. A." last="Iskovskikh">V. A. Iskovskikh</name></author><author><name sortKey="Shur, M G" sort="Shur, M G" uniqKey="Shur M" first="M. G." last="Shur">M. G. Shur</name></author><author><name sortKey="Sevast Anov, V A" sort="Sevast Anov, V A" uniqKey="Sevast Anov V" first="V. A." last="Sevast Anov">V. A. Sevast Anov</name></author><author><name sortKey="Fedenko, A S" sort="Fedenko, A S" uniqKey="Fedenko A" first="A. S." last="Fedenko">A. S. Fedenko</name></author><author><name sortKey="Efimov, B A" sort="Efimov, B A" uniqKey="Efimov B" first="B. A." last="Efimov">B. A. Efimov</name></author><author><name sortKey="Mikhalev, A V" sort="Mikhalev, A V" uniqKey="Mikhalev A" first="A. V." last="Mikhalev">A. V. Mikhalev</name></author><author><name sortKey="Pankrat V, E V" sort="Pankrat V, E V" uniqKey="Pankrat V E" first="E. V." last="Pankrat V">E. V. Pankrat V</name></author><author><name sortKey="Tolpygo, A K" sort="Tolpygo, A K" uniqKey="Tolpygo A" first="A. K." last="Tolpygo">A. K. Tolpygo</name></author><author><name sortKey="Loginov, A I" sort="Loginov, A I" uniqKey="Loginov A" first="A. I." last="Loginov">A. I. Loginov</name></author><author><name sortKey="Ponomarev, D A" sort="Ponomarev, D A" uniqKey="Ponomarev D" first="D. A." last="Ponomarev">D. A. Ponomarev</name></author><author><name sortKey="Shikin, E V" sort="Shikin, E V" uniqKey="Shikin E" first="E. V." last="Shikin">E. V. Shikin</name></author><author><name sortKey="Kydryavtsev, L D" sort="Kydryavtsev, L D" uniqKey="Kydryavtsev L" first="L. D." last="Kydryavtsev">L. D. Kydryavtsev</name></author><author><name sortKey="Kuz Ina, G V" sort="Kuz Ina, G V" uniqKey="Kuz Ina G" first="G. V." last="Kuz Ina">G. V. Kuz Ina</name></author><author><name sortKey="Vasil V, F P" sort="Vasil V, F P" uniqKey="Vasil V F" first="F. P." last="Vasil V">F. P. Vasil V</name></author><author><name sortKey="Arkhangel Ki, A V" sort="Arkhangel Ki, A V" uniqKey="Arkhangel Ki A" first="A. V." last="Arkhangel Ki">A. V. Arkhangel Ki</name></author></analytic><monogr></monogr><series><title level="s">Encyclopaedia of Mathematics</title><imprint><date>1995</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: ϵ-ENTROPY of a set in a metric space - The logarithm to the base 2 of the smallest number of points in an ϵ-net for this set. In other words, the ϵ-entropy ℋϵ(C, X) of a set C lying in a metric space (X, ρ)</div></front></TEI><istex><corpusName>springer-ebooks</corpusName><author><json:item><name>V. M. Tikhomirov</name></json:item><json:item><name>S. A. Stepanov</name></json:item><json:item><name>A. B. Ivanov</name></json:item><json:item><name>L. V. Kantorovich</name></json:item><json:item><name>E. B. Ershov</name></json:item><json:item><name>M. I. Voĭtsekhovskiĭ</name></json:item><json:item><name>V. G. Ushakov</name></json:item><json:item><name>Ya. Yu. Nikitin</name></json:item><json:item><name>M. S. Nikulin</name></json:item><json:item><name>L. D. Kudryavtsev</name></json:item><json:item><name>V. S. Shul’man</name></json:item><json:item><name>N. V. Butenin</name></json:item><json:item><name>T. S. Pigolkina</name></json:item><json:item><name>V. G. Prikazchikov</name></json:item><json:item><name>A. B. Bakushinskiĭ</name></json:item><json:item><name>V. M. Babich</name></json:item><json:item><name>Yu. B. Rudyak</name></json:item><json:item><name>D. D. Sokolov</name></json:item><json:item><name>L. P. Kuptsov</name></json:item><json:item><name>I. A. Kvasnikov</name></json:item><json:item><name>I. N. Vekua</name></json:item><json:item><name>R. A. Kordzadze</name></json:item><json:item><name>Yu. N. Subbotin</name></json:item><json:item><name>O. A. Ivanova</name></json:item><json:item><name>V. N. Grishin</name></json:item><json:item><name>D. A. Suprunenko</name></json:item><json:item><name>A. V. Prokhorov</name></json:item><json:item><name>B. A. Sevast’yanov</name></json:item><json:item><name>A. A. Bukhshtab</name></json:item><json:item><name>V. I. Nechaev</name></json:item><json:item><name>Yu. L. Ershov</name></json:item><json:item><name>M. A. Taĭtslin</name></json:item><json:item><name>E. B. Vinberg</name></json:item><json:item><name>E. D. Solomentsev</name></json:item><json:item><name>Yu. G. Zarkhin</name></json:item><json:item><name>Val. S. Kulikov</name></json:item><json:item><name>M. A. Shubin</name></json:item><json:item><name>V. B. Andreev</name></json:item><json:item><name>N. Kh. Rozov</name></json:item><json:item><name>M. Sh. Tsalenko</name></json:item><json:item><name>L. V. Kuz’min</name></json:item><json:item><name>L. M. Gluskin</name></json:item><json:item><name>Yu. A. Bakhturin</name></json:item><json:item><name>N. N. Vil’yams</name></json:item><json:item><name>V. V. Gorbatsevich</name></json:item><json:item><name>A. F. Leont’ev</name></json:item><json:item><name>E. P. Dolzhenko</name></json:item><json:item><name>R. L. Dobrushin</name></json:item><json:item><name>V. V. Prelov</name></json:item><json:item><name>D. V. Anosov</name></json:item><json:item><name>V. E. Plisko</name></json:item><json:item><name>N. M. Nagornyĭ</name></json:item><json:item><name>S. S. Goncharov</name></json:item><json:item><name>I. A. Lavrov</name></json:item><json:item><name>V. M. Mikheev</name></json:item><json:item><name>V. A. Zalgaller</name></json:item><json:item><name>M. V. Fedoryuk</name></json:item><json:item><name>V. G. Boltyanskiĭ</name></json:item><json:item><name>Ü. Lamiste</name></json:item><json:item><name>L. A. Sidorov</name></json:item><json:item><name>E. M. Semenov</name></json:item><json:item><name>V. P. Petrenko</name></json:item><json:item><name>S. N. Artemov</name></json:item><json:item><name>A. I. Shtern</name></json:item><json:item><name>I. I. 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the smallest number of points in an ϵ-net for this set. 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DisplayOrder="Western"><GivenName>A.</GivenName><GivenName>A.</GivenName><FamilyName>Mal’tsev</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>A.</GivenName><GivenName>D.</GivenName><FamilyName>Myshkis</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>V.</GivenName><GivenName>E.</GivenName><FamilyName>Govorov</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>A.</GivenName><GivenName>L.</GivenName><FamilyName>Onishchik</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>V.</GivenName><GivenName>A.</GivenName><FamilyName>Iskovskikh</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>M.</GivenName><GivenName>G.</GivenName><FamilyName>Shur</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>V.</GivenName><GivenName>A.</GivenName><FamilyName>Sevast’yanov</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>A.</GivenName><GivenName>S.</GivenName><FamilyName>Fedenko</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>B.</GivenName><GivenName>A.</GivenName><FamilyName>Efimov</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>A.</GivenName><GivenName>V.</GivenName><FamilyName>Mikhalev</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>E.</GivenName><GivenName>V.</GivenName><FamilyName>Pankrat’ev</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>A.</GivenName><GivenName>K.</GivenName><FamilyName>Tolpygo</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>A.</GivenName><GivenName>I.</GivenName><FamilyName>Loginov</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>D.</GivenName><GivenName>A.</GivenName><FamilyName>Ponomarev</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>E.</GivenName><GivenName>V.</GivenName><FamilyName>Shikin</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>L.</GivenName><GivenName>D.</GivenName><FamilyName>Kydryavtsev</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>G.</GivenName><GivenName>V.</GivenName><FamilyName>Kuz’mina</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>F.</GivenName><GivenName>P.</GivenName><FamilyName>Vasil’ev</FamilyName></AuthorName></Author><Author><AuthorName DisplayOrder="Western"><GivenName>A.</GivenName><GivenName>V.</GivenName><FamilyName>Arkhangel’skiĭ</FamilyName></AuthorName></Author></AuthorGroup><Abstract ID="Abs1" Language="En" OutputMedium="Online"><Heading>Abstract</Heading><Para>ϵ-<Emphasis Type="Bold">ENTROPY</Emphasis> of a set in a metric space - The logarithm to the base 2 of the smallest number of points in an ϵ-net for this set. In other words, the ϵ-entropy ℋ<Subscript>ϵ</Subscript>(<Emphasis Type="Italic">C</Emphasis>, <Emphasis Type="Italic">X</Emphasis>) of a set <Emphasis Type="Italic">C</Emphasis> lying in a metric space (<Emphasis Type="Italic">X</Emphasis>, ρ)</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>E</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>E</title></titleInfo><name type="personal"><namePart type="given">V.</namePart><namePart type="given">M.</namePart><namePart type="family">Tikhomirov</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">S.</namePart><namePart type="given">A.</namePart><namePart type="family">Stepanov</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart 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type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart type="given">K.</namePart><namePart type="family">Tolpygo</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart type="given">I.</namePart><namePart type="family">Loginov</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">D.</namePart><namePart type="given">A.</namePart><namePart type="family">Ponomarev</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">E.</namePart><namePart type="given">V.</namePart><namePart type="family">Shikin</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">L.</namePart><namePart type="given">D.</namePart><namePart type="family">Kydryavtsev</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">G.</namePart><namePart type="given">V.</namePart><namePart type="family">Kuz’mina</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">F.</namePart><namePart type="given">P.</namePart><namePart type="family">Vasil’ev</namePart><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.</namePart><namePart type="given">V.</namePart><namePart type="family">Arkhangel’skiĭ</namePart><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="research-article" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Springer US</publisher><place><placeTerm type="text">Boston, MA</placeTerm></place><dateIssued encoding="w3cdtf">1995</dateIssued><dateIssued encoding="w3cdtf">1995</dateIssued><copyrightDate encoding="w3cdtf">1995</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: ϵ-ENTROPY of a set in a metric space - The logarithm to the base 2 of the smallest number of points in an ϵ-net for this set. In other words, the ϵ-entropy ℋϵ(C, X) of a set C lying in a metric space (X, ρ)</abstract><relatedItem type="host"><titleInfo><title>Encyclopaedia of Mathematics</title><subTitle>Coproduct — Hausdorff — Young Inequalities</subTitle></titleInfo><name type="personal"><namePart type="given">M.</namePart><namePart type="family">Hazewinkel</namePart><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" displayLabel="Contributed volume" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0G6R5W5T-Z">book-series</genre><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">1995</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11649">Mathematics and Statistics</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="SCM">Mathematics</topic><topic authority="SpringerSubjectCodes" authorityURI="SCM00009">Mathematics, general</topic></subject><identifier type="DOI">10.1007/978-1-4899-3795-7</identifier><identifier type="ISBN">978-0-7923-2974-9</identifier><identifier type="eISBN">978-1-4899-3795-7</identifier><identifier type="BookTitleID">229604</identifier><identifier type="BookID">978-1-4899-3795-7</identifier><identifier type="BookChapterCount">6</identifier><identifier type="BookVolumeNumber">2</identifier><identifier type="BookSequenceNumber">0</identifier><part><date>1995</date><detail type="volume"><number>2</number><caption>vol.</caption></detail><extent unit="pages"><start>415</start><end>548</end></extent></part><recordInfo><recordOrigin>Springer Science+Business Media Dordrecht, 1995</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Encyclopaedia of Mathematics</title></titleInfo><name type="personal"><namePart type="given">M.</namePart><namePart type="family">Hazewinkel</namePart><role><roleTerm type="text">editor</roleTerm></role></name><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">1995</copyrightDate><issuance>serial</issuance></originInfo><identifier type="SeriesID">5920</identifier><recordInfo><recordOrigin>Springer Science+Business Media Dordrecht, 1995</recordOrigin></recordInfo></relatedItem><identifier type="istex">8317721E19D38B916369B37018914CFCDFF37060</identifier><identifier type="ark">ark:/67375/HCB-7B446X0W-J</identifier><identifier type="DOI">10.1007/978-1-4899-3795-7_3</identifier><identifier type="ChapterID">3</identifier><identifier type="ChapterID">Chap3</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer Science+Business Media Dordrecht, 1995</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-3XSW68JL-F">springer</recordContentSource><recordOrigin>Springer Science+Business Media Dordrecht, 1995</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/document/8317721E19D38B916369B37018914CFCDFF37060/metadata/json</uri></json:item></metadata><annexes><json:item><extension>xml</extension><original>true</original><mimetype>application/xml</mimetype><uri>https://api.istex.fr/document/8317721E19D38B916369B37018914CFCDFF37060/annexes/xml</uri></json:item></annexes></istex></record>Pour manipuler ce document sous Unix (Dilib)
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