On Some Properties of Pettis Integrable Multifunctions

We study Aumann-Pettis integrable multifunctions on $2^X$, where X is a separable Banach space and their integrals. We prove the existence of a weakly compact convex-valued Pettis integrable multifunction F for a closed, convex, decomposable and weakly sequentially compact subset K of $P_1(\mu, X)$, the space of all Pettis integrable functions on X such that K coincides with $S_F^P$, the collection of all Pettis integrable selectors of F. We also study the weak compactness property of $S_F^P$.