Strong law of large numbers of Pettis-integrable multifunctions (Q2337139)

Summary: Using reversed martingale techniques, we prove the strong law of large numbres for independent Pettis-integrable multifunctions with convex weakly compact values in a Banach space. The Mosco convergence of reversed Pettis-integrable martingale of the form \((E^{\mathfrak{B}_n} X)_{n \geq 1}\), where \((\mathfrak{B}_n)_{n \geq 1}\) is a decreasing sequence of the sub \(\sigma\)-algebra of \(\mathfrak{F}\) is provided.