Convergence of Conditional Expectations for Unbounded Random Sets, Integrands, and Integral Functionals

Given a sequence of unbounded convex random sets, we study under which conditions Fatou's lemma for the weak upper limit of their conditional expectations holds. We also give multivalued versions of dominated and monotone convergence theorems, and we discuss the special case of the integral. Finally, applications to epigraphic convergence of integrands and to Mosco convergence of certain integral functionals are provided.