The Space of Set-Valued Random Variables

In this text we shall consider the spaces formed by all closed or compact (convex) subsets of a Banach space. We shall call such spaces hyperspaces. Throughout this book, assume that (X, ║ · ║ _X )is a Banach space with the dual space X*, 0 denotes the origin of X, θ denotes the. one element set {0} and ℝ is the set of all of real numbers. The open unit ball in X is denoted by U. Also we shall adopt particular notation for certain classes of subsets of X, which we call hyperspaces.