The Radon-Nikodym problem for approximately proper equivalence relations

The Radon-Nikodym problem for approximately proper equivalence relations

AF-equivalence relations and their cocycles

After a review of some 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.

The Radon-Nikodym Theorem for Reflexive Banach Spaces El Teorema de Radon-Nikodym para Espacios de Banach Reflexivos

In this short paper we prove the equivalence between the RadonNikodym Theorem for reflexive Banach spaces and the representability of weakly compact operators with domain L(μ).

Almost Continuous Orbit Equivalence for Non-singular Homeomorphisms

Let X and Y be Polish spaces with non-atomic Borel measures μ and ν of full support. Suppose that T and S are ergodic non-singular homeomorphisms of (X, μ) and (Y, ν) with continuous Radon-Nikodym derivatives. Suppose that either they are both of type III1 or that they are both of type IIIλ, 0 < λ < 1 and, in the IIIλ case, suppose in addition that both ‘topological asymptotic ranges’ (defined ...

A characterization of sub-riemannian spaces as length dilatation structures constructed via coherent projections

We introduce length dilatation structures on metric spaces, tempered dilatation structures and coherent projections and explore the relations between these objects and the Radon-Nikodym property and Gamma-convergence of length functionals. Then we show that the main properties of sub-riemannian spaces can be obtained from pairs of length dilatation structures, the first being a tempered one and...