Extensions of generic measure-preserving actions
Annales de l'Institut Fourier, Volume 64 (2014) no. 2, p. 607-623

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.

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.

DOI : https://doi.org/10.5802/aif.2859
Classification:  22F10,  54H05,  54E52
Keywords: Measure-preserving action, Baire category, Polish group
@article{AIF_2014__64_2_607_0,
     author = {Melleray, Julien},
     title = {Extensions of generic measure-preserving actions},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {2},
     year = {2014},
     pages = {607-623},
     doi = {10.5802/aif.2859},
     mrnumber = {3330916},
     zbl = {06387286},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2014__64_2_607_0}
}
Melleray, Julien. Extensions of generic measure-preserving actions. Annales de l'Institut Fourier, Volume 64 (2014) no. 2, pp. 607-623. doi : 10.5802/aif.2859. http://www.numdam.org/item/AIF_2014__64_2_607_0/

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