On Almost Sure Convergence of Vector Valued Pramarts and Multivalued Pramarts

Convergence of martingales, amarts, pramarts, mils, have been extentively studied in recent years by a lot of authors: Bellow [3], Blake [4], Chatterji [10], Castaing [5], Castaing and Ezzaki [8], Choukairi ([11], [12], [14]), Daures [15], Bagchi [1], Hiai and Umegaki [20], Hess [19], Egghe ([17], [18]), Millet and Sucheston [26], Lavie [22], Luu ([23], [24], [25]), Slaby [28], Derras [16], Neveu [27], Talagrand [29], and many others. New convergence results for bounded pramarts in $L^1_E$ and in the space $L^1_{wc(E)}$ of integrably bounded multifunction with convex weakly compact values are presented. The main purpose of this paper is to obtain the Linear topology convergence (introduced by Beer [2]) and Mosco-convergence of multivalued pramarts.