THE RADON-NIKODYM THEOREM FOR A NONABSOLUTE INTEGRAL ON MEASURE SPACES

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...

A Radon-nikodym Theorem for Stone Algebra Valued Measures

Introduction. Let C(S) be the ring of continuous real valued functions on a compact Hausdorff space S. Stone [5] shows that each bounded subset of C(S) has a least upper bound (in C(S)) if and only if the closure of each open subset of S is open ; in this event we call C(S) a Stone algebra. Throughout this paper C(S) is a Stone algebra. It is convenient to adjoin an object +00, not in C(S), and...