Serveur d'exploration Bourbaki

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Identifieur interne : 002590 ( Istex/Corpus ); précédent : 002589; suivant : 002591

D

Auteurs : A. G. El In ; M. G. M. Van Doorn ; A. K. Gushchin ; L. D. Kudryavtsev ; V. V. Rumyantsev ; V. I. Sobolev ; B. A. Efimov ; N. Kh. Rozov ; V. T. Bazylev ; I. A. Kvasnikov ; B. I. Golubov ; A. A. Konyushkov ; L. N. Eshukov ; P. P. Korovkin ; A. V. Efimov ; A. A. Zakharov ; S. M. Vorazhin ; Yu. N. Subbotin ; A. L. Onishchik ; D. P. Kostomarov ; N. M. Nagorny ; V. E. Plisko ; N. M. Khalfina ; S. A. Stepanov ; M. S. Nikulin ; S. I. Adyan ; P. S. Soltan ; A. V. Zabrodin ; L. A. Bokut ; S. Yu. Maslov ; G. E. Mints ; E. M. Chirka ; M. V. Fedoryuk ; N. K. Nikol Ki ; B. S. Pavlov ; A. L. Shmel In ; A. V. Arkhangel Ki ; A. B. Bakushinski ; D. A. Ponomarev ; I. V. Dolgachev ; A. A. Boyarkin ; A. V. Mikhalev ; M. I. Vo Tsekhovski ; A. V. Prokhorov ; L. E. Re Zin ; A. M. Il N ; G. N. Dyubin ; D. P. Zhelobenko ; V. P. Chistyakov ; A. V. Khokhlov ; V. A. Dushski ; M. Sh. Farber ; E. D. Solomentsev ; V. D. Kukin ; A. A. Mal Sev ; M. A. Shtan O ; T. P. Lukashenko ; Rédigé Par C. Mayer ; E. M. Nikishin ; B. M. Bredikhin ; R. A. Minlos ; N. G. Ushakov ; V. A. Skvortsov ; V. E. Tarakanov ; V. I. Danilov ; G. P. Tolstov ; D. V. Anosov ; S. N. Artemov ; L. A. Skornyakov ; E. V. Shikin ; I. V. Proskuryakov ; Yu. A. Kuznetsov ; A. B. Ivanov ; V. I. Ponomarev ; A. V. Chernavski ; D. A. Suprunenko ; V. I. Nechaev ; Yu. I. Merzlyakov ; O. A. Ivanova ; V. V. Fedorchuk ; V. L. Popov ; N. A. Karpova ; R. A. Prokhorova ; M. M. Potapov ; V. D. Mazurov ; Yu. B. Rudyak ; A. V. Gulin ; A. A. Samarski ; N. S. Bakhvalov ; L. A. Oganesyan ; Yu. M. Davydov ; V. E. Tarankanov ; A. B. Vasil Va ; E. V. Pankrat V ; R. L. Dobrushin ; V. V. Prelov ; A. A. Dezin ; E. F. Mishchenko ; A. V. Bitsadze ; I. N. Vekua ; A. M. Nakhushev ; I. A. Shishmarev ; E. I. Moiseev ; V. D. Kupradze ; F. P. Vasil V ; N. N. Kuznetsov ; B. L. Rozhdestvenski ; I. P. Makarov ; S. S. Ga Saryan ; A. D. Myshkis ; M. S. Nikol Ki ; A. I. Subbotin ; Ü. Lumiste ; A. V. Pogorelov ; D. V. Alekseevski ; A. F. Filippov ; V. I. Shulikovski ; A. I. Shtern ; S. P. Novikov ; V. A. Morozov ; O. G. Smolyanov ; V. M. Tikhomirov ; V. M. Babich ; V. A. Chuyanov ; L. I. Kamynin ; Yu. A. Rozanov ; V. A. Iskovskikh ; B. A. Pasynkov ; P. S. Aleksandrov ; L. I. Sedov ; D. D. Sokolov ; V. G. Sprindzhuk ; S. M. Voronin ; Yu. V. Matiyasevich ; A. N. Parshin ; V. G. Krechet ; M. Sh. Tsalenko ; A. I. Loginov ; A. F. Lavrik ; L. N. Bol Hev ; A. Yanushauskas ; A. F. Leont V ; E. A. Bredikhina ; I. B. Vapnyarski ; V. M. Solodov ; V. B. Kudryavtsev ; E. B. Vinberg ; A. P. Terekhin ; Yu. I. Zhuravlev ; G. A. Sardanashvili ; S. M. Sirota ; E. G. D Akonov ; E. N. Kuz In ; N. M. Mitrofanova ; A. P. Khusu ; S. K. Sobolev ; V. N. Tutubalin ; V. S. Vladimirov ; V. A. Dorodnitsyn ; I. S. Iokhvidov ; K. S. Swirski ; E. G. Goluzina ; Yu. V. Prokhorov ; V. V. Sazonov ; V. D. Belousov ; D. M. Smirnov ; L. P. Kuptsov ; I. I. Volkov ; L. V. Kuz In ; M. Shirinbekov ; V. N. Grishin ; I. N. Vrublevskaya ; M. M. Popov ; F. A. Kabakov ; A. F. Shapkin ; V. K. Domanski ; G. S. Chogoshvili ; V. P. Palamodov ; A. I. Markusevich ; S. Ya. Khavinson ; A. I. Kostrikin ; A. S. Parkhomenko ; M. I. Vo Sekhovski ; T. S. Fofanova ; W. Glagolev ; E. G. Sklyarenko ; A. A. Kirillov ; K. Bulota ; E. B. Yanovskaya ; I. Kh. Sabitov ; E. G. Sobolevskaya ; L. A. Molotkov ; S. A. Ashmanov ; V. G. Karmanov ; E. N. Berezkin ; A. V. Lykov

Source :

RBID : ISTEX:B76480E9FC4C365C8FB85E94D23264C4CDE24827

Abstract

Abstract: δ-σ-OPERATION - A set-theoretic operation, the result of its application to a sequence (E n ) of sets can be noted thus: φ( E n )= zN nz E n , $$\varphi \left( {E_n } \right) = \bigcup\limits_{z \in N} {\bigcap\limits_{n \in z} {E_n ,} } $$ where N is a system of sets of positive integers, called the base of the δ-σ-operation. See Descriptive set theory.

Url:
DOI: 10.1007/978-1-4899-3795-7_2

Links to Exploration step

ISTEX:B76480E9FC4C365C8FB85E94D23264C4CDE24827

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<name sortKey="Potapov, M M" sort="Potapov, M M" uniqKey="Potapov M" first="M. M." last="Potapov">M. M. Potapov</name>
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<name sortKey="Mazurov, V D" sort="Mazurov, V D" uniqKey="Mazurov V" first="V. D." last="Mazurov">V. D. Mazurov</name>
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<name sortKey="Rudyak, Yu B" sort="Rudyak, Yu B" uniqKey="Rudyak Y" first="Yu. B." last="Rudyak">Yu. B. Rudyak</name>
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<name sortKey="Bakhvalov, N S" sort="Bakhvalov, N S" uniqKey="Bakhvalov N" first="N. S." last="Bakhvalov">N. S. Bakhvalov</name>
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<name sortKey="Oganesyan, L A" sort="Oganesyan, L A" uniqKey="Oganesyan L" first="L. A." last="Oganesyan">L. A. Oganesyan</name>
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<name sortKey="Davydov, Yu M" sort="Davydov, Yu M" uniqKey="Davydov Y" first="Yu. M." last="Davydov">Yu. M. Davydov</name>
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<name sortKey="Tarankanov, V E" sort="Tarankanov, V E" uniqKey="Tarankanov V" first="V. E." last="Tarankanov">V. E. Tarankanov</name>
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<name sortKey="Vasil Va, A B" sort="Vasil Va, A B" uniqKey="Vasil Va A" first="A. B." last="Vasil Va">A. B. Vasil Va</name>
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<front>
<div type="abstract" xml:lang="en">Abstract: δ-σ-OPERATION - A set-theoretic operation, the result of its application to a sequence (E n ) of sets can be noted thus: φ( E n )= zN nz E n , $$\varphi \left( {E_n } \right) = \bigcup\limits_{z \in N} {\bigcap\limits_{n \in z} {E_n ,} } $$ where N is a system of sets of positive integers, called the base of the δ-σ-operation. See Descriptive set theory.</div>
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<abstract>Abstract: δ-σ-OPERATION - A set-theoretic operation, the result of its application to a sequence (E n ) of sets can be noted thus: >m:math display="block"> >m:mrow> >m:mi>φ>/m:mi>>m:mrow>>m:mo>(>/m:mo> >m:mrow> >m:msub> >m:mi>E>/m:mi> >m:mi>n>/m:mi> >/m:msub> >/m:mrow> >m:mo>)>/m:mo>>/m:mrow>>m:mo>=>/m:mo>>m:mstyle displaystyle="true"> >m:munder> >m:mo>∪>/m:mo> >m:mrow> >m:mi>z>/m:mi>>m:mo>∈>/m:mo>>m:mi>N>/m:mi> >/m:mrow> >/m:munder> >m:mrow> >m:mstyle displaystyle="true"> >m:munder> >m:mo>∩>/m:mo> >m:mrow> >m:mi>n>/m:mi>>m:mo>∈>/m:mo>>m:mi>z>/m:mi> >/m:mrow> >/m:munder> >m:mrow> >m:msub> >m:mi>E>/m:mi> >m:mi>n>/m:mi> >/m:msub> >m:mo>,>/m:mo> >/m:mrow> >/m:mstyle> >/m:mrow> >/m:mstyle> >/m:mrow> >/m:math> $$\varphi \left( {E_n } \right) = \bigcup\limits_{z \in N} {\bigcap\limits_{n \in z} {E_n ,} } $$ where N is a system of sets of positive integers, called the base of the δ-σ-operation. See Descriptive set theory.</abstract>
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<p>Abstract: δ-σ-OPERATION - A set-theoretic operation, the result of its application to a sequence (E n ) of sets can be noted thus: φ( E n )= zN nz E n , $$\varphi \left( {E_n } \right) = \bigcup\limits_{z \in N} {\bigcap\limits_{n \in z} {E_n ,} } $$ where N is a system of sets of positive integers, called the base of the δ-σ-operation. See Descriptive set theory.</p>
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<GivenName>G.</GivenName>
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<FamilyName>Berezkin</FamilyName>
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<Abstract ID="Abs1" Language="En" OutputMedium="Online">
<Heading>Abstract</Heading>
<Para>
<Emphasis Type="Bold">δ-σ-OPERATION</Emphasis>
- A set-theoretic operation, the result of its application to a sequence (
<Emphasis Type="Italic">E</Emphasis>
<Subscript>
<Emphasis Type="Italic">n</Emphasis>
</Subscript>
) of sets can be noted thus:
<Equation ID="Equa">
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<EquationSource Format="MATHML"> φ( E n )= zN nz E n , </EquationSource>
<EquationSource Format="TEX">$$\varphi \left( {E_n } \right) = \bigcup\limits_{z \in N} {\bigcap\limits_{n \in z} {E_n ,} } $$</EquationSource>
</Equation>
where
<Emphasis Type="Italic">N</Emphasis>
is a system of sets of positive integers, called the
<Emphasis Type="Italic">base of the</Emphasis>
δ-σ
<Emphasis Type="Italic">-operation.</Emphasis>
See
<Emphasis Type="Bold">Descriptive set theory</Emphasis>
.</Para>
</Abstract>
</ChapterHeader>
<NoBody></NoBody>
</Chapter>
</Book>
</Series>
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<abstract lang="en">Abstract: δ-σ-OPERATION - A set-theoretic operation, the result of its application to a sequence (E n ) of sets can be noted thus: φ( E n )= zN nz E n , $$\varphi \left( {E_n } \right) = \bigcup\limits_{z \in N} {\bigcap\limits_{n \in z} {E_n ,} } $$ where N is a system of sets of positive integers, called the base of the δ-σ-operation. See Descriptive set theory.</abstract>
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