English

On a theorem Dan Rudolph: Part II: Amenable groups

Dynamical Systems 2026-01-07 v1

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 GG-shift (ΛG,σ)(\Lambda^G,\sigma), a typical measure has entropy cc and is Bernoulli. We also address a relative version of this theorem.

Keywords

Cite

@article{arxiv.2601.02939,
  title  = {On a theorem Dan Rudolph: Part II: Amenable groups},
  author = {Tomasz Downarowicz and Jean-Paul Thouvenot and Benjamin Weiss},
  journal= {arXiv preprint arXiv:2601.02939},
  year   = {2026}
}

Comments

16 pages, 1 figure

R2 v1 2026-07-01T08:52:29.688Z