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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.

Extraresolvability of balleans

Igor V. Protasov (2007)

Commentationes Mathematicae Universitatis Carolinae

A ballean is a set endowed with some family of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. We introduce and study a new cardinal invariant of a ballean, the extraresolvability, which is an asymptotic reflection of the corresponding invariant of a topological space.

F σ -mappings and the invariance of absolute Borel classes

Petr Holický, Jiří Spurný (2004)

Fundamenta Mathematicae

It is proved that F σ -mappings preserve absolute Borel classes, which improves results of R. W. Hansell, J. E. Jayne and C. A. Rogers. The proof is based on the fact that any F σ -mapping f: X → Y of an absolute Suslin metric space X onto an absolute Suslin metric space Y becomes a piecewise perfect mapping when restricted to a suitable F σ -set X X satisfying f ( X ) = Y .

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