Abstract
Birkhoff’s theorem asserts that, for an ergodic automorphism, time averages converge to the space average. Krengel showed that, for a given sequence \(\psi(n)\to+0\) and any ergodic automorphism, there exists an indicator function such that the corresponding time means converge a.e. slower than \(\psi\). We give a new proof of the absence of estimates for rates of convergence, answering a question of Podvigin.
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References
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Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 742–746 https://doi.org/10.4213/mzm13810.
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Ryzhikov, V.V. Slow Convergences of Ergodic Averages. Math Notes 113, 704–707 (2023). https://doi.org/10.1134/S0001434623050103
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DOI: https://doi.org/10.1134/S0001434623050103