English

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}
}
R2 v1 2026-06-21T13:58:05.507Z