TY - JOUR

T1 - Quasi-factors and relative entropy for infinite-measure-preserving transformations

AU - Meyerovitch, Tom

N1 - Funding Information:
Acknowledgments. The author thanks Eli Glasner and Benji Weiss for interesting remarks and discussions. This work is a part of his Ph.D at Tel Aviv University. The author owes special thanks to Jon Aaronson, his Ph.D advisor, for valuable guidance and infinite patience, and gratefully acknowledges the support of the Crown Family Foundation Doctoral Fellowships, USA.

PY - 2011/10/1

Y1 - 2011/10/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=80053302974&partnerID=8YFLogxK

U2 - 10.1007/s11856-011-0100-y

DO - 10.1007/s11856-011-0100-y

M3 - Article

AN - SCOPUS:80053302974

VL - 185

SP - 43

EP - 60

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 1

ER -