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

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.

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.

DOI : https://doi.org/10.1214/10-AIHP393
Classification : 37A05,  37A35,  37A40,  28D20
Mots clés : 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},
     pages = {368--376},
     publisher = {Gauthier-Villars},
     volume = {48},
     number = {2},
     year = {2012},
     doi = {10.1214/10-AIHP393},
     zbl = {1269.37003},
     mrnumber = {2954259},
     language = {en},
     url = {http://www.numdam.org/articles/10.1214/10-AIHP393/}
}
Janvresse, Élise; de la Rue, Thierry. Zero Krengel entropy does not kill Poisson entropy. Annales de l'I.H.P. Probabilités et statistiques, Tome 48 (2012) no. 2, pp. 368-376. doi : 10.1214/10-AIHP393. http://www.numdam.org/articles/10.1214/10-AIHP393/

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