Faithful zero-dimensional principal extensions

Tomasz Downarowicz, and Dawid Huczek. "Faithful zero-dimensional principal extensions." Studia Mathematica 212.1 (2012): 1-19. <http://eudml.org/doc/285721>.

@article{TomaszDownarowicz2012,
abstract = {We prove that every topological dynamical system (X,T) has a faithful zero-dimensional principal extension, i.e. a zero-dimensional extension (Y,S) such that for every S-invariant measure ν on Y the conditional entropy h(ν | X) is zero, and, in addition, every invariant measure on X has exactly one preimage on Y. This is a strengthening of the authors' result in Acta Appl. Math. [to appear] (where the extension was principal, but not necessarily faithful).},
author = {Tomasz Downarowicz, Dawid Huczek},
journal = {Studia Mathematica},
keywords = {topological dynamical system; zero-dimensional extension; conditional entropy},
language = {eng},
number = {1},
pages = {1-19},
title = {Faithful zero-dimensional principal extensions},
url = {http://eudml.org/doc/285721},
volume = {212},
year = {2012},
}

TY - JOUR
AU - Tomasz Downarowicz
AU - Dawid Huczek
TI - Faithful zero-dimensional principal extensions
JO - Studia Mathematica
PY - 2012
VL - 212
IS - 1
SP - 1
EP - 19
AB - We prove that every topological dynamical system (X,T) has a faithful zero-dimensional principal extension, i.e. a zero-dimensional extension (Y,S) such that for every S-invariant measure ν on Y the conditional entropy h(ν | X) is zero, and, in addition, every invariant measure on X has exactly one preimage on Y. This is a strengthening of the authors' result in Acta Appl. Math. [to appear] (where the extension was principal, but not necessarily faithful).
LA - eng
KW - topological dynamical system; zero-dimensional extension; conditional entropy
UR - http://eudml.org/doc/285721
ER -