Abstract

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.

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Erik G. F. Thomas

University of Groningen, Department of Mathematics, Postbus 800, 9700 AV Groningen, The Netherlands.

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Suggested citation

E. G. F. Thomas. “Integral Representations in Conuclear Cones.” Journal of Convex Analysis 1 (1994), No. 2, 225–258. https://doi.org/10.68381/jca01016

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Published by Heldermann Verlag, 1994. Rights now held by Banach Press LLC.