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math.DS2019
On lifting invariant probability measures
Tomasz Cieśla
In this note we study when an invariant probability measure lifts to an invariant measure. Consider a standard Borel space , a Borel probability measure on , a Borel map…
math.LO2019
Measurable Hall's theorem for actions of abelian groups
Tomasz Cieśla, Marcin Sabok
We prove a measurable version of the Hall marriage theorem for actions of finitely generated abelian groups. In particular, it implies that for free measure-preserving actions of s…