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Compact Median Algebras are $μ$-Boundaries in a unique way
Uri Bader, Aviv Taller · 2023-10-03 · via math.PR updates on arXiv.org

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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