中文摘要：

假定（X，‖·‖）为实可分的Banach空间，X^n为其对偶空间，（Ω，A，P）为完备的概率空间，{Bn，n≤-1}为上升子σ-域族．讨论了随机集族本性上确界的性质，给出了集值逆Superpramart的逆上鞅逼近及集值逆上鞅在Kuratowski意义下的收敛定理．以此为基础，利用支撑函数证明了集值逆Superpramart在Kuratowski意义与Kuratowski—Mosco意义下的收敛定理，解决了集值逆Superpramart的收敛性问题．

英文摘要：

Let （X, ‖·‖ ） be a real separable Banach space with the dual X^＊ , let （Ω,A,P） be a complete probability space, {Bn, n ≤-1} be an increasing family of subfields of A. Firstly, some properties of random essential supremum are discussed, set-valued inverse superpramart approximation and set-valued inverse superrnartingale convergence theorem in the sense of Kuratowski are provided, respectively. Lastly, set-valued inverse superpramart convergence theorem in the senses Kuratowski and Kuratowski-Mosco are proved, respectively.