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arXiv · 2501.17098

Automorphism groups of measures on the Cantor space. Part I: Good measures and Rokhlin properties

Michal Doucha·Dominik Kwietniak·Maciej Malicki·Piotr Niemiec
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Abstract

We study criteria for the existence of a dense or comeager conjugacy class in the automorphism group of a given measure on the Cantor space. We concentrate on good measures, defined by Akin [\emph{Trans.\ Amer.\ Math.\ Soc.} \textbf{357} (2005), no. 7, 2681--2722], which we characterize as a particular subclass of ultrahomogeneous measures. We determine good measures with rational values on clopen sets whose automorphism group admits a comeager conjugacy class. Our approach uses the Fra\"{i}ss\'{e} theory.

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Michal Doucha, Dominik Kwietniak, Maciej Malicki, Piotr Niemiec. 2025-01-28. Automorphism groups of measures on the Cantor space. Part I: Good measures and Rokhlin properties. https://arxiv.org/abs/2501.17098

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