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Mixing actions of countable groups are almost free

2015
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Proceedings of the American Mathematical Society
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A measure preserving action of a countably innite group Γ is called totally ergodic if every innite subgroup of Γ acts ergodically. For example, all mixing and mildly mixing actions are totally ergodic. This note shows that if an action of Γ is totally ergodic then there exists a nite normal subgroup N of Γ such that the stabilizer of almost every point is equal to N. Surprisingly the proof relies on the group theoretic fact (proved by Hall and Kulatilaka as well as by Kargapolov) that every

doi:10.1090/proc/12467
fatcat:whcrf5eglrhf7iyzsvuz73qm6u