For any 1-1 measure preserving map T of a probability space we can form the [T,Id] and 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 endomorphism is standard.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm155-3-1,
author = {Christopher Hoffman and Daniel Rudolph},
title = {If the [T,Id] automorphism is Bernoulli then the [T,Id] endomorphism is standard},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {195-206},
zbl = {1017.37004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm155-3-1}
}
Christopher Hoffman; Daniel Rudolph. If the [T,Id] automorphism is Bernoulli then the [T,Id] endomorphism is standard. Studia Mathematica, Tome 157 (2003) pp. 195-206. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm155-3-1/