Extensions of generic measure-preserving actions

Julien Melleray (1)

1 AGL - Algèbre, géométrie, logique

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

Mots clés: Measure-preserving action; genericity in the space of actions; extensions of actions

Domaines: Logique [math.LO]; Analyse fonctionnelle [math.FA]

Julien Melleray. Extensions of generic measure-preserving actions. Annales de l'Institut Fourier, 2014. ⟨hal-00661869v2⟩