Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-19T17:41:43.388Z Has data issue: false hasContentIssue false
  • English
  • Français

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: 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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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

Akcoglu, M. A. and del Junco, A., Convergence of averages of point transformations. Proc. Amer. Math. Soc. 49(1975), 265–266.Google Scholar
Azuma, K., Weighted sums of certain dependent random variables. Tohoku Math. J. 19(1967), 357–367.Google Scholar
Bergelson, V., Downarowicz, T., and Misiurewicz, M., A fresh look at the notion of normality. Ann. Sc. Norm. Super. Pisa Cl. Sci., to appear. https://doi.org/10.2422/2036-2145.201808_005Google Scholar
Hoeffding, W., Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58(1963), no. 301, 13–30.Google Scholar
Lindenstrauss, E., Pointwise theorems for amenable groups. Electronic Research Announcements of the AMS 5(1999).Google Scholar