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Analysis reveals nonzero stationary Radon measures for co-compact actions on Hausdorff spaces, indicating structural significance.
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 .
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Alhalimi et al. (2025) studied this question.
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