Conditional expectation of Pettis integrable random sets: existence and convergence theorems

摘要

Existence of the conditional expectation of Pettis integrable random sets is proved. A Representation theorem of Pettis integrable set-valued regular martingales by regular martingales selectors is provided. As applications, Levy's theorem convergence results are studied for Pettis integrable random sets. At the end of this paper, monotone convergence theorem and Fatou's lemma are established for a sequence of conditional expectations of Pettis integrable random sets.