Jointly ergodic measure-preserving transformations

Daniel Berend, Vitaly Bergelson

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

The notion of ergodicity of a measure-preserving transformation is generalized to finite sets of transformations. The main result is that if T 1, T 2, ..., T s are invertible commuting measure-preserving transformations of a probability space (X, ℬ, μ) then {Mathematical expression} for any f 1, f 2, ..., f s∈L x (X, ℬ, μ) iff T 1×T 2×...×T s and all the transformations T iTj 1, i≠j, are ergodic. The multiple recurrence theorem for a weakly mixing transformation follows as a special case.

Original languageEnglish
Pages (from-to)307-314
Number of pages8
JournalIsrael Journal of Mathematics
Volume49
Issue number4
DOIs
StatePublished - 1 Dec 1984
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)

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