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Extensions of generic measure-preserving actions

Julien Melleray (2014)

Annales de l’institut Fourier

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.

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