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The orbital equivalence of Bernoulli actions and their Sinai factors

ZK: Funded in part by ISF grant No. 1570/17.

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  • Given a countable amenable group $ G $ and $ \lambda \in (0,1) $, we give an elementary construction of a type-Ⅲ$ _{\lambda} $ Bernoulli group action. In the case where $ G $ is the integers, we show that our nonsingular Bernoulli shifts have independent and identically distributed factors.

    Mathematics Subject Classification: Primary: 37A40, 37A20; Secondary: 37A35, 60G09.

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