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).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm212-1-1,
author = {Tomasz Downarowicz and Dawid Huczek},
title = {Faithful zero-dimensional principal extensions},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {1-19},
zbl = {1273.37005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm212-1-1}
}
Tomasz Downarowicz; Dawid Huczek. Faithful zero-dimensional principal extensions. Studia Mathematica, Tome 209 (2012) pp. 1-19. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm212-1-1/