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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: leibman@math.ohio-state.edu)
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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

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