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If the $[T, {\rm Id}]$ automorphism is Bernoulli then the $[T, {\rm Id}]$ endomorphism is standard

Tom 155 / 2003

Christopher Hoffman, Daniel Rudolph Studia Mathematica 155 (2003), 195-206 MSC: 28D05, 37A20. DOI: 10.4064/sm155-3-1

Streszczenie

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

Autorzy

  • Christopher HoffmanDepartment of Mathematics
    University of Washington
    Seattle, WA 98195, U.S.A.
    e-mail
  • Daniel RudolphDepartment of Mathematics
    University of Maryland
    College Park, MD 20742, U.S.A.
    e-mail

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