Mosco convergence of set-valued supermartingale

The existence of regular martingale selectors for multivalued supermartingales with unbounded values in a separable Banach space Y is proved. In addition, new convergence results for set-valued supermartingales in the Mosco sense are presented. At the end of this paper, the equivalence between some properties of unbounded set-valued supermartingales and the convergence of these random sets in the Mosco sense is established.