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Decompositions and measures on countable Borel equivalence relations. (arXiv:1801.02767v2 [math.LO] UPDATED)
来源于:arXiv
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. 查看全文>>