On weakly mixing Markov operators and non-singular transformations

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Abstract

Let P be a Markov operator on L(X, Σ, m). Theorem 1: (i) P is weakly mixing ⇔ (ii) For every f∈L there is a sequence {nt} of density 1 such that all w*-cluster points of {Mathematical expression} are constants ⇔ (iii) For every f∈L there is a {kj} with {Mathematical expression}w*-convergent to a constant. Theorem 2: If P is induced by a non-singular transformation θ, P is weakly mixing ⇔ For every AεΣ, {θ-n(A)} has a remotely trivial subsequence. The existence of a finite invariant measure is not required in these results.

Original languageEnglish
Pages (from-to)231-236
Number of pages6
JournalZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Volume55
Issue number2
DOIs
StatePublished - 1 Jun 1981

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Mathematics (all)

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