一族随机集的本性(凸)闭包及其应用(Ⅰ)(英文)

Essential (Convex) Closure of a Family of Random Sets and Its Applications (Ⅰ)

该文定义了一族随机集的本性（凸）闭包并研究了它的性质，利用它证明了更广泛的集值（上，下）鞅的可选标样定理。

In this paper, the essential (convex) closure of a family of random sets is defined and its properties are studied. Using the essential (convex) closure, we prove a more general optional sampling theorem for set - valued (super, sub) martingales.