Henstock-Kurzweil-Pettis integrability of compact valued multifunctions with values in an arbitrary Banach space

The aim of this paper is to describe Henstock-Kurzweil-Pettis (HKP) integrable compact valued multifunctions. Such characterizations are known in case of functions (see Di Piazza and Musiał (2006)  [16]). It is also known (see Di Piazza and Musiał (2010)  [19]) that each HKP-integrable compact valued multifunction can be represented as a sum of a Pettis integrable multifunction and of an HKP-integrable function. Invoking to that decomposition, we present a pure topological characterization of integrability. Having applied the above results, we obtain two convergence theorems, that generalize results known for HKP-integrable functions. We emphasize also the special role played in the theory by weakly sequentially complete Banach spaces and by spaces possessing the Schur property.