2025/07/10 by Petr Naryshkin, Naryshkin, Petr, Andrea Vaccaro +1
Economics, Econometrics and Finance · Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #Economic theories and models #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2507.07891
openalex publication_date 2025/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the notions of u-amenability and hyper-u-amenability for countable Borel equivalence relations, strong forms of amenability that are implied by hyperfiniteness. We show that treeable, hyper-u-amenable countable Borel equivalence relations are hyperfinite. One of the corollaries that we get is that if a countable Borel equivalence relation is measure-hyperfinite and equal to the orbit equivalence relation of a free continuous action of a virtually free group on a σ-compact Polish space, then it is hyperfinite. We also obtain that if a countable Borel equivalence relation is treeable and equal to the orbit equivalence relation of a Borel action of an amenable group on a standard Borel space, or if it is treeable, amenable and Borel bounded, then it is hyperfinite.