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2019 Extreme partitions of a Lebesgue space and their application in topological dynamics
Wojciech Bułatek, Brunon Kamiński, Jerzy Szymański
Topol. Methods Nonlinear Anal. 53(2): 447-455 (2019). DOI: 10.12775/TMNA.2019.007

Abstract

It is shown that any topological action $\Phi$ of a countable orderable and amenable group $G$ on a compact metric space $X$ and every $\Phi$-invariant probability Borel measure $\mu$ admit an extreme partition $\zeta$ of $X$ such that the equivalence relation $R_{\zeta}$ associated with $\zeta$ contains the asymptotic relation $A(\Phi)$ of $\Phi$. As an application of this result and the generalized Glasner theorem it is proved that $A(\Phi)$ is dense for the set $E_{\mu}(\Phi)$ of entropy pairs.

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Wojciech Bułatek. Brunon Kamiński. Jerzy Szymański. "Extreme partitions of a Lebesgue space and their application in topological dynamics." Topol. Methods Nonlinear Anal. 53 (2) 447 - 455, 2019. https://doi.org/10.12775/TMNA.2019.007

Information

Published: 2019
First available in Project Euclid: 9 May 2019

zbMATH: 07130706
MathSciNet: MR3983981
Digital Object Identifier: 10.12775/TMNA.2019.007

Rights: Copyright © 2019 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.53 • No. 2 • 2019
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