Weak convergence and weak compactness for multifunctions with values in a separable Banach space

Abstract

In this paper we extend the notion of weak convergence to Banach space valued integrable multifunctions. We prove some properties of this mode of convergence and we show that under certain hypotheses the space of uniformly bounded, w w -compact, convex valued integrable multifunctions is sequentially weakly complete. Then we prove two Dunford-Pettis type weak compactness theorems and we also show that the set valued conditional expectation is weakly continuous. Finally we present an application from control theory.