no. 2
Extensions of generic measure-preserving actions
[Extensions d’actions préservant une mesure de probabilité]
Melleray, Julien1
1 Université de Lyon CNRS UMR 5208 Institut Camille Jordan 43 boulevard du 11 novembre 1918 69622 Villeurbanne Cedex (France)
Annales de l'Institut Fourier, Tome 64 (2014) no. 2, pp. 607-623.

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.

DOI : 10.5802/aif.2859
Classification : 22F10, 54H05, 54E52
Keywords: Measure-preserving action, Baire category, Polish group
Mot clés : action préservant une mesure de probabilité, méthodes de Baire, groupe polonais

Melleray, Julien 1

1 Université de Lyon CNRS UMR 5208 Institut Camille Jordan 43 boulevard du 11 novembre 1918 69622 Villeurbanne Cedex (France) 
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Melleray, Julien. Extensions of generic measure-preserving actions. Annales de l'Institut Fourier, Tome 64 (2014) no. 2, pp. 607-623. doi : 10.5802/aif.2859. https://aif.centre-mersenne.org/articles/10.5802/aif.2859/

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