The starting point of this paper is a recent work. of de Korvin – Kleyle (Stoch Anal. Appl. 3 (1985)) on the convergence of set valued supermartingales with values in a separable Banach space. Since their motivation is to model information systems with goal uncertainty, they introduce the spmg–convergence. Here we present another version of this theorem with a different type of convergence. In fact in finite dimensions this mode is convergence in the Eausdroffmetric. Finally i we generalize to set valued quasimartingales