Integral Representations in Conuclear Cones

We show that closed convex cones, having bounded order intervals (in particular weakly complete proper convex cones) in conuclear spaces, are generated by their extreme rays. An analogue of Choquet’s theorem is obtained for these cones, as well as for the conuclear cones defined in this article. Well-capped cones are conuclear. The main tool is Choquet’s notion of conical measure, of which we present the necessary properties here.