2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62663After a review of some of the main results about hyperfinite equivalence relations and their cocycles in the measured setting, we give a definition of a topological AF-equivalence relation. We show that every cocycle is cohomologous to a quasi-product cocycle. We then study the problem of determining the quasi-invariant probability measures admitting a given cocycle as their Radon-Nikodym derivative.15 pages, talk at 4th International Conference on Operator Algebras, July 2-7 2001, Constanza, RomaniaOperator AlgebrasDynamical Systems46L55; 43A35text