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arXiv · 2406.02401

Spatial models for boolean actions in the infinite measure-preserving setup

Fabien Hoareau·François Le Maître
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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: L\'evy groups cannot admit nontrivial continuous measure-preserving actions on Polish spaces when the measure is locally finite.

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Fabien Hoareau, François Le Maître. 2024-06-04. Spatial models for boolean actions in the infinite measure-preserving setup. https://arxiv.org/abs/2406.02401

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