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.
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The authors thank the referee, who proposed a simplification of the initial proof of Theorem 1.
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Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 1, pp. 40–52.
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Kachurovskii, A.G., Podvigin, I.V. Measuring the Rate of Convergence in the Birkhoff Ergodic Theorem. Math Notes 106, 52–62 (2019). https://doi.org/10.1134/S0001434619070058
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DOI: https://doi.org/10.1134/S0001434619070058