Spatial models for boolean actions in the infinite measure-preserving setup
Abstract
We show that up to a null set, every infinite measure-preserving action of a locally compact Polish group can be turned into a continuous measure-preserving action on a locally compact Polish space where the underlying measure is Radon. We also investigate the distinction between spatial and boolean actions in the infinite measure-preserving setup. In particular, we extend Kwiatkowska and Solecki’s Point Realization Theorem to the infinite measure setup. We finally obtain a streamlined proof of a recent result of Avraham-Re’em and Roy: Lévy groups cannot admit non-trivial continuous measure-preserving actions on Polish spaces when the measure is locally finite.
Fields of Study & Subjects
Advanced Topology and Set Theory
Mathematical Dynamics and Fractals
Advanced Operator Algebra Research
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Volume
- 379
- Issue
- 6
- Pages
- 4263–4305
- Publication date
- 28 January 2026
- Language
- EN