Topologies on measure spaces and the Radon-Nikodym theorem

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).

A Reformulation of the Radon-nikodym Theorem

The Radon-Nikodym theorems of Segal and Zaanen are principally concerned with the classification of those measures p. for which any X« p. is given in the form

A Radon-Nikodym approach to measure information

Differentiability of Lipschitz Maps from Metric Measure Spaces to Banach Spaces with the Radon Nikodym Property

In this paper we prove the differentiability of Lipschitz maps X → V , where X is a complete metric measure space satisfying a doubling condition and a Poincaré inequality, and V denotes a Banach space with the Radon Nikodym Property (RNP). The proof depends on a new characterization of the differentiable structure on such metric measure spaces, in terms of directional derivatives in the direct...

Analogue of Lebesgue-Radon-Nikodym Theorem with respect to p-adic q-Measure on Zp

and Applied Analysis 3 By 2.2 , we get μf,−q ( a pZp ) 2 q 2 qp −qa ∫ Zp f ( a px ) dμ−qpn x . 2.3 Therefore, by 2.3 , we obtain the following theorem. Theorem 2.1. For f, g ∈ C Zp , one has μαf βg,−q αμf,−q βμg,−q, 2.4 where α, β are constants. From 2.2 and 2.4 , we note that ∣μf,−q ( a pZp )∣∣ ≤ M‖f‖∞, 2.5 where ‖f‖∞ supx∈Zp |f x | and M is some positive constant. Now, we recall the definitio...