Convergence of conditional expectations for unbounded random sets, integrands, and integral functionals

Given a sequence of unbounded convex random sets, conditions are studied under which Fatou’s lemma for the weak upper limit of their conditional expectations holds. Multivalued versions of dominated and monotone convergence theorems are also given, and the special case of the integral is discussed. Finally, applications to epigraphic convergence of integrands and to Mosco convergence of certain integral functionals are provided.