AF-equivalence relations and their cocycles

2001/11/15 by Jean Renault, Renault, Jean
Mathematics · #43A35 #46L55 #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA) #math.DS #math.OA #msc:43A35 #msc:46L55

paper · pdf · doi:10.48550/arxiv.math/0111182

15 pages, talk at 4th International Conference on Operator Algebras, July 2-7 2001, Constanza, Romania

arxiv created 2001/11/15 · arxiv updated 2009/11/30

Abstract

After 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.

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