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Ergodic measures on compact metric spaces for isometric actions by inductively compact groups


Author: Yanqi Qiu
Journal: Proc. Amer. Math. Soc. 145 (2017), 1593-1598
MSC (2010): Primary 37A25; Secondary 28A33
DOI: https://doi.org/10.1090/proc/13371
Published electronically: October 3, 2016
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Abstract: We obtain a partial converse of Vershik's description of ergodic probability measures on a compact metric space with respect to an isometric action by an inductively compact group. This allows us to identify, in this setting, the set of ergodic probability measures with the set of weak limit points of orbital measures. We also show that for a general action of an inductively compact group, the weak limit of orbital measures can fail to be ergodic.


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Additional Information

Yanqi Qiu
Affiliation: CNRS, Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse Cedex 9, France
Email: yqi.qiu@gmail.com

DOI: https://doi.org/10.1090/proc/13371
Received by editor(s): February 29, 2016
Received by editor(s) in revised form: May 25, 2016
Published electronically: October 3, 2016
Additional Notes: This work is supported by the grant IDEX UNITI - ANR-11-IDEX-0002-02, financed by Programme “Investissements d’Avenir” of the government of the French Republic managed by the French National Research Agency.
Communicated by: Nimish Shah
Article copyright: © Copyright 2016 American Mathematical Society