Faithful zero-dimensional principal extensions

Volume 212 / 2012

Tomasz Downarowicz, Dawid Huczek Studia Mathematica 212 (2012), 1-19 MSC: Primary 37A35; Secondary 37B10. DOI: 10.4064/sm212-1-1

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 $\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).

Authors

  • Tomasz DownarowiczInstitute of Mathematics and Computer Science
    Wrocław Institute of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail
  • Dawid HuczekInstitute of Mathematics and Computer Science
    Wrocław Institute of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail

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