2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222334For a type II_1 ergodic measured equivalence relation R on a probability space without atom, we prove that h(R)=2C(R)-2, where C(R) is the cost, and h(R) the isoperimetric constant. This follows recent result by Lyons and the authors.5 pagesOperator AlgebrasDynamical SystemsGroup Theorytext