Compact Median Algebras are μ-Boundaries in a unique way

2023/10/03 by Bader, Uri, Taller, Aviv · 1 citation
#FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR) #Probability (math.PR)

paper · doi:10.48550/arxiv.2310.02024

Abstract

We consider group actions on compact median algebras. We show that, given a generating probability measure μ on the acting group and under suitable conditions on the median algebra, it could be realized in a unique way as a μ-boundary in the sense of Furstenberg. Along the way, we prove some structural results.

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• Cocycle superrigidity for median spaces of finite rank

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