This article studies convex integral functionals of the form EIh(v) = E

This article gives dual representations for convex integral function-als on the linear space of regular processes. This space turns out to be a Banach space containing many more familiar classes of stochastic pro-cesses and its dual is identified with the space of optional Radon measures with essentially bounded variation. Combined with classical Banach space techniques, our results allow for systematic treatment of a large class of optimization problems from optimal stopping to singular stochastic con