Extensions of generic measure-preserving actions

Melleray, Julien

Extensions of generic measure-preserving actions
[Extensions d’actions préservant une mesure de probabilité]

Annales de l'Institut Fourier, Tome 64 (2014), p. 607-623 / Harvested from Numdam

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Résumé
Abstract

Nous établissons que, pour tout groupe dénombrable abélien $Γ$ et tout sous-groupe finiment engendré $Δ$ de $Γ$ , l’ensemble des actions de $Δ$ sur un espace de probabilités standard $(X, μ)$ qui peuvent être étendues en une action libre de $Γ$ sur $(X, μ)$ est générique (au sens de Baire). Ce résultat étend un théorème d’Ageev, qui correspond au cas où $Δ$ est un groupe cyclique infini.

We show that, whenever $Γ$ is a countable abelian group and $Δ$ is a finitely-generated subgroup of $Γ$ , a generic measure-preserving action of $Δ$ on a standard atomless probability space $(X, μ)$ extends to a free measure-preserving action of $Γ$ on $(X, μ)$ . This extends a result of Ageev, corresponding to the case when $Δ$ is infinite cyclic.

Publié le : 2014-01-01

MR 3330916 | Zbl 06387286

DOI : https://doi.org/10.5802/aif.2859
Classification: 22F10, 54H05, 54E52
Mots clés: action préservant une mesure de probabilité, méthodes de Baire, groupe polonais

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     author = {Melleray, Julien},
     title = {Extensions of generic measure-preserving actions},
     journal = {Annales de l'Institut Fourier},
     volume = {64},
     year = {2014},
     pages = {607-623},
     doi = {10.5802/aif.2859},
     zbl = {06387286},
     mrnumber = {3330916},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2014__64_2_607_0}
}

Melleray, Julien. Extensions of generic measure-preserving actions. Annales de l'Institut Fourier, Tome 64 (2014) pp. 607-623. doi : 10.5802/aif.2859. http://gdmltest.u-ga.fr/item/AIF_2014__64_2_607_0/

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