Random sets and Choquet-type representations

As appropriate generalizations of convex combinations with uncountably many terms, we introduce the so-called Choquet combinations, decomposable and as well their corresponding hull operators acting on power sets Lebesgue-Bochner spaces. We show that coincides in finite-dimensional setting, yet tends to be larger infinite dimensions. also provide a quantitative characterization hull, without any topological or algebraic assumptions underlying set. Furthermore, set its strongly closed hull. It turns out measurable selections closed-valued multifunction form those convex-valued Finally, investigate operator-type features when applied succession.