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Edited to weaken the conjecture.
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Vladimir
Vladimir
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Hyperfinite equivalence relations are treeable. For the case of uncountable relations, I was wondering if there is a reference to (or simple proof of) the following statement: Let $E$ be a (possibly uncountable) amenable equivalence relation on a standard probability space $(X,\mu)$. IfThen $E$ is not treeable then it is equal (mod $\mu$) to $X \times X$. Or perhaps is this statement incorrect?

Hyperfinite equivalence relations are treeable. For the case of uncountable relations, I was wondering if there is a reference to (or simple proof of) the following statement: Let $E$ be a (possibly uncountable) amenable equivalence relation on a standard probability space $(X,\mu)$. If $E$ is not treeable then it is equal (mod $\mu$) to $X \times X$.

Hyperfinite equivalence relations are treeable. For the case of uncountable relations, I was wondering if there is a reference to (or simple proof of) the following statement: Let $E$ be a (possibly uncountable) amenable equivalence relation on a standard probability space $(X,\mu)$. Then $E$ is treeable. Or perhaps is this statement incorrect?

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Vladimir
Vladimir
  • 1.3k
  • 9
  • 18

Equivalence relations that are both not treeable and amenable

Hyperfinite equivalence relations are treeable. For the case of uncountable relations, I was wondering if there is a reference to (or simple proof of) the following statement: Let $E$ be a (possibly uncountable) amenable equivalence relation on a standard probability space $(X,\mu)$. If $E$ is not treeable then it is equal (mod $\mu$) to $X \times X$.