Measure Reducibility of Countable Borel Equivalence Relations
نویسندگان
چکیده
We show that every basis for the countable Borel equivalence relations strictly above E0 under measure reducibility is uncountable, thereby ruling out natural generalizations of the Glimm-Effros dichotomy. We also push many known results concerning the abstract structure of the measure reducibility hierarchy to its base, using arguments substantially simpler than those previously employed.
منابع مشابه
Countable Borel equivalence relations, Borel reducibility, and orbit equivalence
ing from the proof given above for Gaboriau-Popa we obtain theorems such as: Theorem 2.10 Let (X, d) be a complete, separable metric space equipped with an atomless Borel probability measure μ. Suppose Γ acts ergodically by measure preserving transformations on (X,μ) and the action on (X, d) is expansive. Let (Et)0<t<1 be a collection of distinct countable Borel equivalence relations on X with:...
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