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Minimal model-universal flows for locally compact Polish groups (2006.01710v1)

Published 2 Jun 2020 in math.DS, math.GR, and math.LO

Abstract: Let $G$ be a locally compact Polish group. A metrizable $G$-flow $Y$ is called model-universal if by considering the various invariant probability measures on $Y$, we can recover every free action of $G$ on a standard Lebesgue space up to isomorphism. Weiss has shown that for countable $G$, there exists a minimal, model-universal flow. In this paper, we extend this result to all locally compact Polish groups.