We show that, whenever is a countable abelian group and is a finitely-generated subgroup of , a generic measure-preserving action of on a standard atomless probability space extends to a free measure-preserving action of on . This extends a result of Ageev, corresponding to the case when is infinite cyclic.
Nous établissons que, pour tout groupe dénombrable abélien et tout sous-groupe finiment engendré de , l’ensemble des actions de sur un espace de probabilités standard qui peuvent être étendues en une action libre de sur est générique (au sens de Baire). Ce résultat étend un théorème d’Ageev, qui correspond au cas où est un groupe cyclique infini.
Keywords: Measure-preserving action, Baire category, Polish group
Mot clés : action préservant une mesure de probabilité, méthodes de Baire, groupe polonais
Melleray, Julien 1
@article{AIF_2014__64_2_607_0, author = {Melleray, Julien}, title = {Extensions of generic measure-preserving actions}, journal = {Annales de l'Institut Fourier}, pages = {607--623}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {64}, number = {2}, year = {2014}, doi = {10.5802/aif.2859}, mrnumber = {3330916}, zbl = {06387286}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2859/} }
TY - JOUR AU - Melleray, Julien TI - Extensions of generic measure-preserving actions JO - Annales de l'Institut Fourier PY - 2014 SP - 607 EP - 623 VL - 64 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2859/ DO - 10.5802/aif.2859 LA - en ID - AIF_2014__64_2_607_0 ER -
%0 Journal Article %A Melleray, Julien %T Extensions of generic measure-preserving actions %J Annales de l'Institut Fourier %D 2014 %P 607-623 %V 64 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2859/ %R 10.5802/aif.2859 %G en %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.2859/
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