If the [ T , Id ] automorphism is Bernoulli then the [ T , Id ] endomorphism is standard
نویسندگان
چکیده
For any 1-1 measure preserving map T of a probability space we can form the [T, Id] and [T, T−1] automorphisms as well as the corresponding endomorphisms and decreasing sequence of σ-algebras. In this paper we show that if T has zero entropy and the [T, Id] automorphism is isomorphic to a Bernoulli shift then the decreasing sequence of σ-algebras generated by the [T, Id] endomorphism is standard. We also show that if T has zero entropy and the [T 2, Id] automorphism is isomorphic to a Bernoulli shift then the decreasing sequence of σ-algebras generated by the [T, T−1] endomorphism is standard.
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