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
