Almost sure convergence of set-valued martingales and submartingales (Q1207364)

We prove that if \((X_ n)_{n\geq 1}\) is a set-valued martingale (or submartingale) taking values from the family of all nonempty, closed, convex, bounded subsets of a reflexive, separable Banach space satisfying ``\(L^ 1\)-bounded'' condition, e.g., \(\sup_ nE| X_ n|<\infty\), then \(X_ n\) converges almost surely in Mosco sense.