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arXiv · 2601.02939

On a theorem Dan Rudolph: Part II: Amenable groups

Tomasz Downarowicz·Jean-Paul Thouvenot·Benjamin Weiss
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Abstract

We prove an analog of Rudolph's theorem for actions of countable amenable groups, which asserts that among invariant measures with entropy at least c on the $G$-shift $(\Lambda^G,\sigma)$, a typical measure has entropy $c$ and is Bernoulli. We also address a relative version of this theorem.

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Tomasz Downarowicz, Jean-Paul Thouvenot, Benjamin Weiss. 2026-01-06. On a theorem Dan Rudolph: Part II: Amenable groups. https://arxiv.org/abs/2601.02939

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