Measurable multifunctions in nonseparable Banach spaces

In this article we define measurable multifunctions in nonseparable Banach spaces, prove a weak compactness criterion for the selectors of multifunctions integrably bounded, characterize Banach spaces that have the Radon-Nikodym property by means of convergence of multivalued martingales, generalize some recent results on convergence of set-valued conditional expectations, and give some applications to control theory and differential inclusions.