Michael Selections and Castaing Representations with càdlàg Functions

Abstract It follows from Michael’s selection theory that a closed convex nonempty-valued mapping the Sorgenfrey line to euclidean space is inner semicontinuous if and only can be represented as image closure of right-continuous selections mapping. This article gives necessary sufficient conditions for representation hold càdlàg selections, i.e., are have left limits. The characterization motivated by continuous time stochastic optimization problems over processes. Here, an application integral functionals functions given.