Volume 6 (2023)
Melleray, Julien; Robert, Simon
From invariant measures to orbit equivalence, via locally finite groups
Annales Henri Lebesgue, Volume 6 (2023), pp. 259-295.

Metadata

DOI10.5802/ahl.165
Keywords Orbit equivalence, Cantor dynamics, minimal actions, ample groups

Abstract

We give a new proof of a theorem of Giordano, Putnam and Skau characterizing orbit equivalence of minimal homeomorphisms of the Cantor space in terms of their sets of invariant Borel probability measures. The proof is based on a strengthening of a theorem of Krieger concerning minimal actions of certain locally finite groups of homeomorphisms, and we also give a new proof of the Giordano–Putnam–Skau characterization of orbit equivalence for these actions.


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