Abstract: Let （X,‖·‖） be a real separable Banach space with the dual X^*, (Ω, B ,P) be a complete probability s pace, further, {B_n, n≥1} be a increase sub σ-fields filtration of B , and B=∨B_n, we proved the Riesz approximation theorem of setvalued martingales in the limit, and made use of the results present the convergence theorenm of setvalued martingales in the limit.

Key words: setvalued martingales in the limit, Riesz approxim ation theorem, KuratowskiMosco convergence, Kuratowski convergence, weak convergence