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 $\nu $ on $Y$ the conditional entropy $h(\nu\,|\, X)$ 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).
Keywords:
prove every topological dynamical system has faithful zero dimensional principal extension zero dimensional extension every s invariant measure conditional entropy zero addition every invariant measure has exactly preimage strengthening authors result acta appl math appear where extension principal necessarily faithful
Affiliations des auteurs :
Tomasz Downarowicz
1
;
Dawid Huczek
1
1
Institute of Mathematics and Computer Science Wrocław Institute of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
@article{10_4064_sm212_1_1,
author = {Tomasz Downarowicz and Dawid Huczek},
title = {Faithful zero-dimensional principal extensions},
journal = {Studia Mathematica},
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year = {2012},
volume = {212},
number = {1},
doi = {10.4064/sm212-1-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm212-1-1/}
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AU - Dawid Huczek
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Tomasz Downarowicz; Dawid Huczek. Faithful zero-dimensional principal extensions. Studia Mathematica, Tome 212 (2012) no. 1, pp. 1-19. doi: 10.4064/sm212-1-1
