Geodesic
Faithful zero-dimensional principal extensions
Tomasz Downarowicz 1   ; Dawid Huczek 1
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 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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 
@article{10_4064_sm212_1_1,
     author = {Tomasz Downarowicz and Dawid Huczek},
     title = {Faithful zero-dimensional principal extensions},
     journal = {Studia Mathematica},
     pages = {1--19},
     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/}
}
TY  - JOUR
AU  - Tomasz Downarowicz
AU  - Dawid Huczek
TI  - Faithful zero-dimensional principal extensions
JO  - Studia Mathematica
PY  - 2012
SP  - 1
EP  - 19
VL  - 212
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm212-1-1/
DO  - 10.4064/sm212-1-1
LA  - en
ID  - 10_4064_sm212_1_1
ER  - 
%0 Journal Article
%A Tomasz Downarowicz
%A Dawid Huczek
%T Faithful zero-dimensional principal extensions
%J Studia Mathematica
%D 2012
%P 1-19
%V 212
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/sm212-1-1/
%R 10.4064/sm212-1-1
%G en
%F 10_4064_sm212_1_1
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

Cité par Sources :