If the $[T, {\rm Id}]$ automorphism is Bernoulli
then the $[T, {\rm Id}]$ endomorphism is standard
Studia Mathematica, Tome 155 (2003) no. 3, pp. 195-206
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Mots-clés :
measure preserving map probability space form automorphisms corresponding endomorphisms decreasing sequence sigma algebras paper has zero entropy automorphism isomorphic bernoulli shift decreasing sequence sigma algebras generated endomorphism standard has zero entropy automorphism isomorphic bernoulli shift decreasing sequence sigma algebras generated endomorphism standard
Affiliations des auteurs :
Christopher Hoffman 1 ; Daniel Rudolph 2
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title = {If the $[T, {\rm Id}]$ automorphism is {Bernoulli
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Christopher Hoffman; Daniel Rudolph. If the $[T, {\rm Id}]$ automorphism is Bernoulli
then the $[T, {\rm Id}]$ endomorphism is standard. Studia Mathematica, Tome 155 (2003) no. 3, pp. 195-206. doi: 10.4064/sm155-3-1
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