Hyperfinite measure-preserving actions of countable groups and their model theory
Abstract
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.
Fields of Study & Subjects
Advanced Topology and Set Theory
advanced mathematical theories
Mathematical and Theoretical Analysis
Publication details
- Journal / source
- Journal of Logic and Analysis
- Publisher
- Journal of Logic and Analysis
- Volume
- 18
- Publication date
- 29 April 2026
- Language
- EN