ON MULTIVALUED MARTINGALES WHOSE VALUES MAY BE UNBOUNDED - MARTINGALE SELECTORS AND MOSCO CONVERGENCE

Using classical results on the projective limit of a sequence of subsets, we show the existence of martingale selectors for a multivalued martingale (and supermartingale) with closed values in a separable Banach space X. The existence of L1(X)-bounded or uniformly integrable martingale selectors is also discussed. At last, applications to the Mosco convergence of multivalued supermartingales and supermartingale integrands are provided. © 1991.