Rational weak mixing in infinite measure spaces

Abstract

Rational weak mixing is a measure theoretic version of Krickeberg's strong ratio mixing property for infinite measure preserving transformations. It requires "{\tt 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.

Typos in the definitions of "rational weak mixing" and "weak rational ergodicity" (p.5) are corrected

References in corpus (1)

• Operator renewal theory and mixing rates for dynamical systems with infinite measure

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• On the problem by Erdös-de Bruijn-Kingman on regularity of reciprocals for exponential series