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Zero Krengel entropy does not kill Poisson entropy

Élise Janvresse, Thierry de la Rue (2012)

Annales de l'I.H.P. Probabilités et statistiques

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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