Zero Krengel entropy does not kill Poisson entropy
Annales de l'I.H.P. Probabilités et statistiques, Volume 48 (2012) no. 2, p. 368-376

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.

Nous prouvons que les notions d'entropie de Krengel et d'entropie de Poisson pour les transformations préservant une mesure infinie ne coïncident pas toujours : nous construisons une transformation conservative préservant une mesure infinie qui a une entropie de Krengel nulle (la transformation induite sur un ensemble de mesure 1 est l'odomètre de Von Neumann-Kakutani), mais dont la suspension de Poisson a une entropie strictement positive.

DOI : https://doi.org/10.1214/10-AIHP393
Classification:  37A05,  37A35,  37A40,  28D20
Keywords: Krengel entropy, Poisson suspension, infinite-measure-preserving transformation, d̄-distance
@article{AIHPB_2012__48_2_368_0,
     author = {Janvresse, \'Elise and de la Rue, Thierry},
     title = {Zero Krengel entropy does not kill Poisson entropy},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {48},
     number = {2},
     year = {2012},
     pages = {368-376},
     doi = {10.1214/10-AIHP393},
     zbl = {1269.37003},
     mrnumber = {2954259},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2012__48_2_368_0}
}
Janvresse, Élise; de la Rue, Thierry. Zero Krengel entropy does not kill Poisson entropy. Annales de l'I.H.P. Probabilités et statistiques, Volume 48 (2012) no. 2, pp. 368-376. doi : 10.1214/10-AIHP393. http://www.numdam.org/item/AIHPB_2012__48_2_368_0/

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