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- W2783157730 abstract "Abstract We show that the uniform measure-theoretic ergodic decomposition of a countable Borel equivalence relation $(X, E)$ may be realized as the topological ergodic decomposition of a continuous action of a countable group $Gamma curvearrowright X$ generating E . We then apply this to the study of the cardinal algebra $mathcal {K}(E)$ of equidecomposition types of Borel sets with respect to a compressible countable Borel equivalence relation $(X, E)$ . We also make some general observations regarding quotient topologies on topological ergodic decompositions, with an application to weak equivalence of measure-preserving actions." @default.
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- W2783157730 date "2020-12-04" @default.
- W2783157730 modified "2023-10-17" @default.
- W2783157730 title "Decompositions and measures on countable Borel equivalence relations" @default.
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- W2783157730 doi "https://doi.org/10.1017/etds.2020.119" @default.
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