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October 2011 Comparability of clopen sets in a zero-dimensional dynamical system
Hisatoshi Yuasa
Proc. Japan Acad. Ser. A Math. Sci. 87(8): 123-127 (October 2011). DOI: 10.3792/pjaa.87.123

Abstract

Let $\varphi$ be a homeomorphism on a totally disconnected, compact metric space $X$. We introduce a binary relation on the family of clopen subsets of $X$, which is described in terms of the $\varphi$-invariant probability measures. We show that $\varphi$ is uniquely ergodic if and only if any two clopen subsets of $X$ are comparable with respect to the binary relation.

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Hisatoshi Yuasa. "Comparability of clopen sets in a zero-dimensional dynamical system." Proc. Japan Acad. Ser. A Math. Sci. 87 (8) 123 - 127, October 2011. https://doi.org/10.3792/pjaa.87.123

Information

Published: October 2011
First available in Project Euclid: 3 October 2011

zbMATH: 1246.37023
MathSciNet: MR2843091
Digital Object Identifier: 10.3792/pjaa.87.123

Subjects:
Primary: ‎37B05‎
Secondary: 37A55

Keywords: Bratteli-Vershik system , countable Hopf-equivalence , ordered Bratteli diagram , totally ordered group , unique ergodicity

Rights: Copyright © 2011 The Japan Academy

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Vol.87 • No. 8 • October 2011
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