Zero Krengel Entropy does not kill Poisson Entropy

Details Zero Krengel Entropy does not kill Poisson Entropy Zero Krengel Entropy does not kill Poisson Entropy

2009-10-14

arxiv.org/abs/0910.2566v2

Transactions of the American Mathematical Society 362 (2010) pp. 3069-3094

Mathematics

Probability

Scientific paper

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.

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