Rational weak mixing in infinite measure spaces (Q2873999)
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scientific article; zbMATH DE number 6251094
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Rational weak mixing in infinite measure spaces |
scientific article; zbMATH DE number 6251094 |
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Rational weak mixing in infinite measure spaces (English)
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28 January 2014
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rational weak mixing
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conservative transformation
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infinite measure preserving
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\textit{K. Krickeberg} [in: Proc. 5th Berkeley Symp. Math. Stat. Probab., Univ. Calif. 1965/66, 2, Part 2, 431--446 (1967; Zbl 0211.48503)] introduced a notion of topological ratio mixing for infinite measure preserving Markov chains. Here an abstract measure-theoretic analogue, rational weak mixing, is defined using a density ratio convergence for every pair of measurable sets in some dense hereditary ring. It is shown that this property implies weak rational ergodicity and spectral weak mixing. Examples are shown with this property, and it is shown that the power and subsequence versions of the property hold generically.
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