We consider Borel measures on a locally compact Hausdorff space whose values are linear functionals on a locally convex cone. We define integrals for cone-valued functions and verify that continuous linear functionals on certain spaces of continuous cone-valued functions endowed with an inductive limit topology may be represented by such integrals.
"A Riesz representation theorem for cone-valued functions." Abstr. Appl. Anal. 4 (4) 209 - 229, 1999. https://doi.org/10.1155/S1085337599000160