Non-compact versions of Edwards' Theorem

Edwards' Theorem establishes duality between a convex cone in the space of continuous functions on a compact space X and the set of representing or Jensen measures for this cone. It is a direct consequence of the description of positive superlinear functionals on C(X). In this paper we obtain the description of such functionals when X is a locally compact sigma-compact Hausdorff space. As a consequence we prove non-compact versions of Edwards' Theorem.