2005/03/09 by Damien Gaboriau, Gaboriau, Damien
Mathematics · #05C25 #05C80 #20E #20E05 #20E06 #20F65 #37A20 #46L10 #82B43 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Operator Algebras (math.OA) #Probability (math.PR) #math.DS #math.GR #math.OA #math.PR #msc:05C25 #msc:05C80 #msc:20E #msc:20E05 #msc:20E06 #msc:20F65 #msc:37A20 #msc:46L10 #msc:82B43
paper · pdf · doi:10.48550/arxiv.math/0503181
To appear in Ergodic Theory and Dynamical Systems
openalex publication_date 2005/03/09 · arxiv created 2005/05/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Measure Equivalence (ME) is the measure theoretic counterpart of quasi-isometry. This field grew considerably during the last years, developing tools to distinguish between different ME classes of countable groups. On the other hand, contructions of ME equivalent groups are very rare. We present a new method, based on a notion of measurable free-factor, and we apply it to exhibit a new family of groups that are measure equivalent to the free group. We also present a quite extensive survey on results about Measure Equivalence for countable groups.