Measuring the Rate of Convergence in the Birkhoff Ergodic Theorem

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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.

Original languageEnglish
Pages (from-to)52-62
Number of pages11
JournalMathematical Notes
Issue number1-2
Publication statusPublished - 1 Jul 2019


  • individual ergodic theorem
  • lattice
  • rate of convergence in ergodic theorems
  • return time
  • unimprovability of estimates


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