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

• Autorzy: Christopher Hoffman , Daniel Rudolph
• Języki publikacji: 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.

Kategorie tematyczne

• 37A20: Orbit equivalence, cocycles, ergodic equivalence relations
• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 155
• Numer: 3
• Strony: 195-206

Daty

wydano

2003

Twórcy

autor

Christopher Hoffman

• Department of Mathematics, University of Washington, Seattle, WA 98195, U.S.A.

autor

Daniel Rudolph

• Department of Mathematics, University of Maryland, College Park, MD 20742, U.S.A.

Identyfikatory

DOI

10.4064/sm155-3-1