Infinite stationary measures of co‐compact group actions
Abstract Let be a finitely generated group, and let be a nondegenerate, finitely supported probability measure on . We show that every co‐compact action on a locally compact Hausdorff space admits a nonzero ‐stationary Radon measure. The main ingredient of the proof is a stationary analog of Tarski's theorem: we show that for every nonempty subset there is a ‐stationary, finitely additive measure on that assigns unit mass to .
Authors
- Tianyi Zheng (ORCID: https://orcid.org/0000-0001-7132-3358)
- Omer Tamuz (ORCID: https://orcid.org/0000-0002-0111-0418)
- Minghao Pan (ORCID: https://orcid.org/0000-0001-9584-8343)
- Mohammedsaid Alhalimi
- Tom Hutchcroft
Institutions
- California Institute of Technology (US)
- University of California San Diego (US)
- University of California, Berkeley (US)
Publication Details
- Journal
- Bulletin of the London Mathematical Society
- Published
- 2025-09-23
- DOI
- https://doi.org/10.1112/blms.70198
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00