Measurability with Distances of Spaces of Functions and Radon-Nikodym Indexes

Abstract

We study the measurability and integrability of the weak upper limit of a sequence of multifunctions .The Pettis integral and measurability with selections of multifunctions in Banach spaces was shown.The largest class of closed convex valued multifunctions which explain the coincide between Effros measurability and scalar measurability are investigaled . Applications of measure of weak noncompactness under complex and real interpolation and some classes of operators in the theory of functional equations in the large Lebesgue space and Banach spaces are obtained .Radon–Nikodym indexes and measures of weak noncompactness with real interpolation of operators are discussed