Abstract: Let （X,‖·‖） be a real separable Banach space with the dual X^*, (Ω,B,P) be a complete probability space, further, {B_n,n≥1} is an increase sub σ-field filtration of B, and B=∨B_n, we discussedsome properties of setvalued martingale in the limit, then used support function and Riesz decomposition theorem of real valued martingale in the limit to prove its Riesz decomposition theorem.

Key words: setvalued L¹ martingale in the limit, potential, Riesz decomposition