Compact Median Algebras are $\mu$-Boundaries in a unique way

Uri Bader; Aviv Taller

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arXiv · 2310.02024

Compact Median Algebras are $\mu$-Boundaries in a unique way

Uri Bader·Aviv Taller

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Abstract

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

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Uri Bader, Aviv Taller. 2023-10-03. Compact Median Algebras are $\mu$-Boundaries in a unique way. https://arxiv.org/abs/2310.02024

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