# Decompositions and measures on countable Borel equivalence relations

@article{Chen2020DecompositionsAM, title={Decompositions and measures on countable Borel equivalence relations}, author={Ruiyuan Chen}, journal={Ergodic Theory and Dynamical Systems}, year={2020}, volume={41}, pages={3671 - 3703} }

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…

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