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Rational weak mixing in infinite measure spaces

Published online by Cambridge University Press:  31 August 2012

JON AARONSON
JON AARONSON*
Affiliation:
School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel (email: aaro@post.tau.ac.il)
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Abstract

Rational weak mixing is a measure theoretic version of Krickeberg’s strong ratio mixing property for infinite measure preserving transformations. It requires ‘density’ ratio convergence for every pair of measurable sets in a dense hereditary ring. Rational weak mixing implies weak rational ergodicity and (spectral) weak mixing. It is enjoyed for example by Markov shifts with Orey’s strong ratio limit property. The power, subsequence version of the property is generic.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 33 , Issue 6 , December 2013 , pp. 1611 - 1643
Copyright
Copyright © 2012 Cambridge University Press 

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