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      Measurable Hall's theorem for actions of abelian groups

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          Abstract

          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, M\'ath\'e and Pikhurko on the measurable circle squaring and confirms a special case of a conjecture of Gardner.

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          Countable abelian group actions and hyperfinite equivalence relations

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            Baire measurable paradoxical decompositions via matchings

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              Closed sets without measurable matching

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                Author and article information

                Journal
                07 March 2019
                Article
                1903.02987
                458c09be-d883-41a0-b89c-03b16c4a4411

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                math.LO math.CO math.MG

                Combinatorics,Geometry & Topology,Logic & Foundation
                Combinatorics, Geometry & Topology, Logic & Foundation

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