Topological Methods in Nonlinear Analysis

Extreme partitions of a Lebesgue space and their application in topological dynamics

Wojciech Bułatek, Brunon Kamiński, and Jerzy Szymański

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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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Topol. Methods Nonlinear Anal., Volume 53, Number 2 (2019), 447-455.

First available in Project Euclid: 9 May 2019

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Bułatek, Wojciech; Kamiński, Brunon; Szymański, Jerzy. Extreme partitions of a Lebesgue space and their application in topological dynamics. Topol. Methods Nonlinear Anal. 53 (2019), no. 2, 447--455. doi:10.12775/TMNA.2019.007.

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