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If the [T,Id] automorphism is Bernoulli then the [T,Id] endomorphism is standard

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Hoffman C., Rudolph D.

Studia Mathematica

2003

tom 155

nr 3

195-206

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 [T²,Id] automorphism is isomorphic to a Bernoulli shift then the decreasing sequence of σ-algebras generated by the $[T,T^{-1}]$ endomorphism is standard.

Ograniczanie wyników

1 Studia Mathematica

1 Hoffman C.

1 Rudolph D.

1 2003

Wyniki wyszukiwania

If the [T,Id] automorphism is Bernoulli then the [T,Id] endomorphism is standard