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A Comment on Ergodic Theorem for Amenable Groups

Part of: Ergodic theory

Published online by Cambridge University Press:  29 July 2019

Bartosz Frej Open the ORCID record for Bartosz Frej [Opens in a new window]  and
Dawid Huczek Open the ORCID record for Dawid Huczek [Opens in a new window]
Bartosz Frej
Affiliation:
Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland. Email: [email protected]@pwr.edu.pl
Dawid Huczek
Affiliation:
Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland. Email: [email protected]@pwr.edu.pl
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Abstract

We prove a version of the ergodic theorem for an action of an amenable group, where a Følner sequence need not be tempered. Instead, it is assumed that a function satisfies certain mixing conditions.

Keywords

amenable groupgroup actionconcentration inequalityergodic average

MSC classification

Primary: 37A15: General groups of measure-preserving transformations
Secondary: 37A30: Ergodic theorems, spectral theory, Markov operators
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 2 , June 2020 , pp. 257 - 261
Copyright
© Canadian Mathematical Society 2019

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Footnotes

Research of both authors is supported from resources for science in years 2013–2018 as research project (NCN grant 2013/08/A/ST1/00275, Poland)

References

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