Trees and amenable equivalence relations

Scot Adams

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

Abstract

Let R be a Borel equivalence relation with countable equivalence classes on a measure space M. Intuitively, a “treeing“of R is a measurably-varying way of makin each equivalence class into the vertices of a tree. We make this definition rigorous. We prove that if each equivalence class becomes a tree with polynomial growth, then the equivalence relation is amenable. We prove that if the equivalence relation is finite measure-preserving and amenable, then almost every tree (i.e., equivalence class) must have one or two ends.

Original languageEnglish (US)
Pages (from-to)1-14
Number of pages14
JournalErgodic Theory and Dynamical Systems
Volume10
Issue number1
DOIs
StatePublished - Mar 1990

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