English

Hyperfinite actions on countable sets and probability measure spaces

Group Theory 2011-07-12 v3 Functional Analysis

Abstract

We introduce the notion of hyperfiniteness for permutation actions of countable groups on countable sets and give a geometric and analytic characterization, similar to the known characterizations for amenable actions. We also answer a question of van Douwen on actions of the free group on two generators on countable sets.

Keywords

Cite

@article{arxiv.1105.3200,
  title  = {Hyperfinite actions on countable sets and probability measure spaces},
  author = {Miklos Abert and Gabor Elek},
  journal= {arXiv preprint arXiv:1105.3200},
  year   = {2011}
}

Comments

19 pages, added a more general result and corrected typos

R2 v1 2026-06-21T18:08:09.162Z