Measurable Hall's theorem for actions of abelian groups

Speaker(s)

Tomasz Cieśla

Affiliation

McGill University

Date

May 22, 2019, 4:15 p.m.

Room

room 5050

Seminar

Topology and Set Theory Seminar

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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 such groups, if two equidistributed measurable sets are equidecomposable, then they are equidecomposable using measurable pieces. The latter generalizes a recent result of Grabowski, Máthé and Pikhurko on the measurable circle squaring and confirms a special case of a conjecture of Gardner. This is joint work with Marcin Sabok.

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