Quasi-factors for infinite-measure preserving transformations

Details Quasi-factors for infinite-measure preserving transformations Quasi-factors for infinite-measure preserving transformations

2008-06-18

arxiv.org/abs/0806.2967v1

Mathematics

Dynamical Systems

13 pages

Scientific paper

This paper is a study of Glasner's definition of quasi-factors in the setting of infinite-measure preserving system. 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. Following and extending Glasner and Weiss, we also prove that any conservative measure preserving system with positive entropy in the sense of Danilenko and Rudolph admits any probability preserving system with positive entropy as a factor. Some applications and connections with Poisson-suspensions are presented.

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