Groups, Geometry, and Dynamics


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Volume 11, Issue 2, 2017, pp. 567–583
DOI: 10.4171/GGD/408

Published online: 2017-06-26

Minimal models for actions of amenable groups

Bartosz Frej[1] and Dawid Huczek[2]

(1) Wroclaw University of Science & Technology, Poland
(2) Wrocław University of Science & Technology, Poland

We prove that on a metrizable, compact, zero-dimensional space every free action of an amenable group is measurably isomorphic to a minimal $G$-action with the same, i.e. affinely homeomorphic, simplex of measures.

Keywords: Topologicalmodel, dynamical system, group action, amenable group, invariant measure, Choquet simplex, Borel isomorphism

Frej Bartosz, Huczek Dawid: Minimal models for actions of amenable groups. Groups Geom. Dyn. 11 (2017), 567-583. doi: 10.4171/GGD/408