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Mat. Zametki, 2019, Volume 106, Issue 1, Pages 40–52 (Mi mz11817)  

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

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.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm11817

Full text: PDF file (527 kB)
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English version:
Mathematical Notes, 2019, 106:1, 52–62

Bibliographic databases:

UDC: 517.987+519.216
Received: 04.10.2017
Revised: 08.10.2018

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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  • https://doi.org/10.4213/mzm11817
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