Hyperfinite measure-preserving actions of countable groups and their model theory

Alice Giraud

Hyperfinite measure-preserving actions of countable groups and their model theory

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arxiv 1910.07985 v2 pith:XVY2IFXF submitted 2019-10-17 math.DS math.GRmath.LO

Alice Giraud This is my paper · ORCID

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keywords actionscountablehyperfinitemeasure-preservingprobabilityspacesgroupsmodel

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We give a shorter proof of a theorem of G. Elek stating that two hyperfinite measure-preserving actions of a countable group on standard probability spaces are approximately conjugate if and only if they have the same invariant random subgroup. We then use this theorem to study model theory of hyperfinite measure-preserving actions of countable groups on probability spaces. This work generalizes the model-theoretic study of automorphisms of probability spaces conducted by I. Ben Yaacov, A. Berenstein, C. W. Henson and A. Usvyatsov.

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Relative Property (T), simplices of invariant measures, and existentially closed models
math.LO 2026-08 conditional novelty 7.0 of 10

A transitive permutation group whose point stabilizer has relative Property (T) yields a Bauer or Poulsen simplex of invariant measures, with the Bauer case characterized by Property (T) of the group.

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