A constructive version of Birkhoff's ergodic theorem for Martin-Lof random points
Identifieur interne : 001D03 ( Main/Exploration ); précédent : 001D02; suivant : 001D04A constructive version of Birkhoff's ergodic theorem for Martin-Lof random points
Auteurs : Laurent Bienvenu [France] ; Adam Day [États-Unis] ; Mathieu Hoyrup [France] ; Ilya Mezhirov [Allemagne] ; Alexander Shen [France]Source :
- Information and Computation [ 0890-5401 ] ; 2012.
English descriptors
- mix :
Abstract
A theorem of Kucera states that given a Martin-Löf random infinite binary sequence {\omega} and an effectively open set A of measure less than 1, some tail of {\omega} is not in A. We first prove several results in the same spirit and generalize them via an effective version of a weak form of Birkhoff's ergodic theorem. We then use this result to get a stronger form of it, namely a very general effective version of Birkhoff's ergodic theorem, which improves all the results previously obtained in this direction, in particular those of V'Yugin, Nandakumar and Hoyrup, Rojas.
Url:
DOI: 10.1016/j.ic.2011.10.006
Affiliations:
Links toward previous steps (curation, corpus...)
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Le document en format XML
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<orgName>Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier</orgName>
<orgName type="acronym">LIRMM</orgName>
<date type="start">1995</date>
<desc><address><addrLine>CC 477, 161 rue Ada, 34095 Montpellier Cedex 5</addrLine>
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</address>
<ref type="url">http://www.lirmm.fr</ref>
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<tutelle name="UMR5506" active="#struct-410122" type="indirect"><org type="institution" xml:id="struct-410122" status="VALID"><orgName>Université de Montpellier</orgName>
<orgName type="acronym">UM</orgName>
<desc><address><addrLine>163 rue Auguste Broussonnet - 34090 Montpellier</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.umontpellier.fr/</ref>
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<idno type="ISNI">0000000122597504</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
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</address>
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</hal:affiliation>
<country>France</country>
</affiliation>
</author>
</analytic>
<idno type="DOI">10.1016/j.ic.2011.10.006</idno>
<series><title level="j">Information and Computation</title>
<idno type="ISSN">0890-5401</idno>
<imprint><date type="datePub">2012</date>
</imprint>
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<profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>Algorithmic randomness</term>
<term>Birkhoff's ergodic theorem</term>
<term>Martin-Löf randomness</term>
<term>Poincaré recurrence theorem</term>
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<front><div type="abstract" xml:lang="en">A theorem of Kucera states that given a Martin-Löf random infinite binary sequence {\omega} and an effectively open set A of measure less than 1, some tail of {\omega} is not in A. We first prove several results in the same spirit and generalize them via an effective version of a weak form of Birkhoff's ergodic theorem. We then use this result to get a stronger form of it, namely a very general effective version of Birkhoff's ergodic theorem, which improves all the results previously obtained in this direction, in particular those of V'Yugin, Nandakumar and Hoyrup, Rojas.</div>
</front>
</TEI>
<affiliations><list><country><li>Allemagne</li>
<li>France</li>
<li>États-Unis</li>
</country>
<region><li>Grand Est</li>
<li>Lorraine (région)</li>
</region>
<settlement><li>Metz</li>
<li>Nancy</li>
</settlement>
<orgName><li>Université de Lorraine</li>
</orgName>
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<tree><country name="France"><noRegion><name sortKey="Bienvenu, Laurent" sort="Bienvenu, Laurent" uniqKey="Bienvenu L" first="Laurent" last="Bienvenu">Laurent Bienvenu</name>
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<name sortKey="Hoyrup, Mathieu" sort="Hoyrup, Mathieu" uniqKey="Hoyrup M" first="Mathieu" last="Hoyrup">Mathieu Hoyrup</name>
<name sortKey="Shen, Alexander" sort="Shen, Alexander" uniqKey="Shen A" first="Alexander" last="Shen">Alexander Shen</name>
</country>
<country name="États-Unis"><noRegion><name sortKey="Day, Adam" sort="Day, Adam" uniqKey="Day A" first="Adam" last="Day">Adam Day</name>
</noRegion>
</country>
<country name="Allemagne"><noRegion><name sortKey="Mezhirov, Ilya" sort="Mezhirov, Ilya" uniqKey="Mezhirov I" first="Ilya" last="Mezhirov">Ilya Mezhirov</name>
</noRegion>
</country>
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