A non-singular dynamical system without maximal ergodic inequality

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:469

Article

el Abdalaoui, E. H.¹ 

[1] Univ Rouen Normandy, LMRS UMR CNRS UNIV 60 85, Dept Math, Ave Univ,BP 12, F-76801 St Etienne Du Rouvray, France

关键词: Ergodic theorems;    Non-singular maps;    Furstenberg ergodic averages;    Birkhoff theorem;    Strictly ergodic topological model;    Joining;   

DOI  :  10.1016/j.jmaa.2018.09.046

来源: Elsevier

【 摘 要 】

It is shown that there is a non-singular dynamical system for which the maximal ergodic inequality does not hold. We further discuss the connection between a non-singular dynamical systems and the pointwise convergence of the Furstenberg ergodic averages. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free