Geodesic
Faithful zero-dimensional principal extensions
Tomasz Downarowicz1 ; Dawid Huczek1
1 Institute of Mathematics and Computer Science Wrocław Institute of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
Studia Mathematica, Tome 212 (2012) no. 1, pp. 1-19

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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).
DOI : 10.4064/sm212-1-1
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

Tomasz Downarowicz 1 ; Dawid Huczek 1

1 Institute of Mathematics and Computer Science Wrocław Institute of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland 
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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

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