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Matematicheskie Zametki, 2019, Volume 106, Issue 1, Pages 40–52
DOI: https://doi.org/10.4213/mzm11817 (Mi mzm11817) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Measuring the Rate of Convergence in the Birkhoff Ergodic Theorem

A. G. Kachurovskiiab, I. V. Podviginab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Full-text PDF (527 kB) Citations (10)
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DOI: https://doi.org/10.4213/mzm11817
Abstract: Estimates of the rate of convergence in the Birkhoff ergodic theorem which hold almost everywhere are considered. For the action of an ergodic automorphism, the existence of such estimates is proved, their structure is studied, and unimprovability questions are considered.
Keywords: individual ergodic theorem, rate of convergence in ergodic theorems, unimprovability of estimates, return time, lattice.
Received: 04.10.2017
Revised: 08.10.2018
English version:
Mathematical Notes, 2019, Volume 106, Issue 1, Pages 52–62
DOI: https://doi.org/10.1134/S0001434619070058
Bibliographic databases:
Document Type: Article
UDC: 517.987+519.216
Language: Russian
Citation: A. G. Kachurovskii, I. V. Podvigin, “Measuring the Rate of Convergence in the Birkhoff Ergodic Theorem”, Mat. Zametki, 106:1 (2019), 40–52; Math. Notes, 106:1 (2019), 52–62
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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