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

Christopher Hoffman, and Daniel Rudolph. "If the [T,Id] automorphism is Bernoulli then the [T,Id] endomorphism is standard." Studia Mathematica 155.3 (2003): 195-206. <http://eudml.org/doc/285090>.

@article{ChristopherHoffman2003,
abstract = {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.},
author = {Christopher Hoffman, Daniel Rudolph},
journal = {Studia Mathematica},
keywords = {endomorphism; entropy; automorphism; Bernoulli shift},
language = {eng},
number = {3},
pages = {195-206},
title = {If the [T,Id] automorphism is Bernoulli then the [T,Id] endomorphism is standard},
url = {http://eudml.org/doc/285090},
volume = {155},
year = {2003},
}

TY - JOUR
AU - Christopher Hoffman
AU - Daniel Rudolph
TI - If the [T,Id] automorphism is Bernoulli then the [T,Id] endomorphism is standard
JO - Studia Mathematica
PY - 2003
VL - 155
IS - 3
SP - 195
EP - 206
AB - 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.
LA - eng
KW - endomorphism; entropy; automorphism; Bernoulli shift
UR - http://eudml.org/doc/285090
ER -