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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 FrejOpen the ORCID record for Bartosz Frej[Opens in a new window] and
Dawid HuczekOpen 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: Bartosz.Frej@pwr.edu.plDawid.Huczek@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: Bartosz.Frej@pwr.edu.plDawid.Huczek@pwr.edu.pl
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Abstract

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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

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 2 , June 2020, pp. 257 - 261
Copyright
© Canadian Mathematical Society 2019

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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