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Free minimal actions of countable groups with invariant probability measures

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  20 February 2020

GÁBOR ELEK
GÁBOR ELEK*
Affiliation:
Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster, LA1 4YF, UK email [email protected]
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Abstract

We prove that for any countable group $\unicode[STIX]{x1D6E4}$, there exists a free minimal continuous action $\unicode[STIX]{x1D6FC}:\unicode[STIX]{x1D6E4}\curvearrowright {\mathcal{C}}$ on the Cantor set admitting an invariant Borel probability measure.

Keywords

free minimal actionsuniformly recurrent subgroupsinvariant measures

MSC classification

Primary: 46L55: Noncommutative dynamical systems
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 5 , May 2021 , pp. 1369 - 1389
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Copyright
© The Author(s) 2020. Published by Cambridge University Press

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