Indecomposability of treed equivalence relations

Research paper by Scot Adams

Indexed on: 01 Dec '88Published on: 01 Dec '88Published in: Israel Journal of Mathematics


We define rigorously a “treed” equivalence relation, which, intuitively, is an equivalence relation together with a measurably varying tree structure on each equivalence class. We show, in the nonamenable, ergodic, measure-preserving case, that a treed equivalence relation cannot be stably isomorphic to a direct product of two ergodic equivalence relations.