Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T17:58:19.874Z Has data issue: false hasContentIssue false
  • English
  • Français

Lower bounds for ergodic averages

Published online by Cambridge University Press:  19 June 2002

A. LEIBMAN
A. LEIBMAN
Affiliation:
Department of Mathematics, Ohio State University, 232 W 18th Avenue, Columbus, OH 43210, USA (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We compute the exact lower bounds for some averages arising in ergodic theory. In particular, we prove that for any measure-preserving system (X,\mathcal{B},\mu,T) with \mu(X)<\infty, any A\in\mathcal{B} and any N\in\mathbb{N}, N^{-1}\sum_{n=0}^{N-1}\mu(A\cap T^{-n}A)\geq\sqrt{\mu(A)^{2}+(\mu(X)-\mu(A))^{2}}+\mu(A)-\mu(X).

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 3 , June 2002 , pp. 863 - 872
Copyright
2002 Cambridge University Press

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.)