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Minimal topological actions do not determine the measurable orbit equivalence class

Gábor Elek·Tullio Ceccherini-Silberstein
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Abstract

We construct a minimal topological action $\wp$ of a non-amenable group on a Cantor set $C$, which is non-uniquely ergodic and furthermore there exist ergodic invariant measures $μ_1$ and $μ_2$ such that $(\wp,C,μ_1)$ and $(\wp,C,μ_2)$ are not orbit equivalent measurable equivalence relations.

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Gábor Elek, Tullio Ceccherini-Silberstein. 2006-08-25. Minimal topological actions do not determine the measurable orbit equivalence class. https://arxiv.org/abs/math/0608629

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