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• # Artykuł - szczegóły

## Studia Mathematica

2003 | 155 | 3 | 195-206

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

EN

### Abstrakty

EN
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.

195-206

wydano
2003

### Twórcy

autor
• Department of Mathematics, University of Washington, Seattle, WA 98195, U.S.A.
autor
• Department of Mathematics, University of Maryland, College Park, MD 20742, U.S.A.