We prove that on a metrizable, compact, zero-dimensional space every free action of an amenable group is measurably isomorphic to a minimal -action with the same, i.e. affinely homeomorphic, simplex of measures.
Cite this article
Bartosz Frej, Dawid Huczek, Minimal models for actions of amenable groups. Groups Geom. Dyn. 11 (2017), no. 2, pp. 567–583DOI 10.4171/GGD/408