Quasi-factors and relative entropy for infinite-measure-preserving transformations

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Abstract

We extend the definition of quasi-factors for infinite-measure-preserving transformations. The existence of a system with zero Krengel entropy and a quasi-factor with positive entropy is obtained. On the other hand, relative zero-entropy for conservative systems implies relative zero-entropy of any quasi-factor with respect to its natural projection onto the factor. This extends (and is based upon) results of Glasner, Thouvenot and Weiss [6, 7]. Following and extending Glasner and Weiss [8], we also prove that any conservative measure-preserving system with positive entropy in the sense of Danilenko and Rudolph [3] admits any probability-preserving system with positive entropy as a factor. Some applications and connections with Poisson-suspensions are presented.

Original languageEnglish
Pages (from-to)43-60
Number of pages18
JournalIsrael Journal of Mathematics
Volume185
Issue number1
DOIs
StatePublished - 1 Oct 2011
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)

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