  As appropriate generalizations of convex combinations with uncountably many
terms, we introduce the so-called Choquet combinations, Choquet decompositions
and Choquet convex decompositions, as well as their corresponding hull
operators acting on the power sets of Lebesgue-Bochner spaces. We show that
Choquet hull coincides with convex hull in the finite-dimensional setting, yet
Choquet hull tends to be larger in infinite dimensions. We also provide a
quantitative characterization of Choquet hull. Furthermore, we show that
Choquet decomposable hull of a set coincides with its (strongly) closed
decomposable hull and the Choquet convex decomposable hull of a set coincides
with its Choquet decomposable hull of the convex hull. It turns out that the
collection of all measurable selections of a closed-valued multifunction is
Choquet decomposable and those of a closed convex-valued multifunction is
Choquet convex decomposable. Finally, we investigate the operator-type features
of Choquet decomposable and Choquet convex decomposable hull operators when
applied in succession.

Functional Analysis;Probability