Zero Krengel Entropy does not kill Poisson Entropy
Probability
2012-11-20 v2 Dynamical Systems
Abstract
We prove that the notions of Krengel entropy and Poisson entropy for infinite-measure-preserving transformations do not always coincide: We construct a conservative infinite-measure-preserving transformation with zero Krengel entropy (the induced transformation on a set of measure 1 is the Von Neumann-Kakutani odometer), but whose associated Poisson suspension has positive entropy.
Keywords
Cite
@article{arxiv.0910.2566,
title = {Zero Krengel Entropy does not kill Poisson Entropy},
author = {Élise Janvresse and Thierry De La Rue},
journal= {arXiv preprint arXiv:0910.2566},
year = {2012}
}