A cone-theoretic barycenter existence theorem
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We show that every continuous valuation on a locally convex, locally convex-compact, sober topological cone ℭ has a barycenter. This barycenter is unique, and the barycenter map β is continuous, hence is the structure map of a 𝐕_w-algebra, i.e., an Eilenberg-Moore algebra of the extended valuation monad on the category of T_0 topological spaces; it is, in fact, the unique 𝐕_w-algebra that induces the cone structure on ℭ.
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