[Des mesures invariantes à l’équivalence orbitale, en passant par des groupes localement finis]
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.
Nous donnons une nouvelle preuve d’un théorème de Giordano, Putnam et Skau qui caractérise l’équivalence orbitale d’homéomorphismes minimaux de l’espace de Cantor à l’aide de leurs ensembles de mesures de probabilité boréliennes invariantes. La preuve est basée sur une amélioration d’un théorème de Krieger, qui s’applique aux actions minimales de certains groupes d’homéomorphismes localement finis. Nous donnons également une nouvelle preuve du théorème de Giordano–Putnam–Skau caractérisant l’équivalence orbitale pour de telles actions.
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Keywords: Orbit equivalence, Cantor dynamics, minimal actions, ample groups
Melleray, Julien 1 ; Robert, Simon 1
CC-BY 4.0
@article{AHL_2023__6__259_0,
author = {Melleray, Julien and Robert, Simon},
title = {From invariant measures to orbit equivalence, via locally finite groups},
journal = {Annales Henri Lebesgue},
pages = {259--295},
year = {2023},
publisher = {\'ENS Rennes},
volume = {6},
doi = {10.5802/ahl.165},
language = {en},
url = {https://numdam.org/articles/10.5802/ahl.165/}
}
TY - JOUR AU - Melleray, Julien AU - Robert, Simon TI - From invariant measures to orbit equivalence, via locally finite groups JO - Annales Henri Lebesgue PY - 2023 SP - 259 EP - 295 VL - 6 PB - ÉNS Rennes UR - https://numdam.org/articles/10.5802/ahl.165/ DO - 10.5802/ahl.165 LA - en ID - AHL_2023__6__259_0 ER -
Melleray, Julien; Robert, Simon. From invariant measures to orbit equivalence, via locally finite groups. Annales Henri Lebesgue, Tome 6 (2023), pp. 259-295. doi: 10.5802/ahl.165
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