Two theorems of functional analysis effectively equivalent to choice axioms
An extension of Choquet boundary theory to certain partially ordered compact convex sets
Characterizing infinite dimensional manifolds topologically
A simple proof in Monge-Kantorovich duality theory
A simple proof is given of a Monge-Kantorovich duality theorem for a lower bounded lower semicontinuous cost function on the product of two completely regular spaces. The proof uses only the Hahn-Banach theorem and some properties of Radon measures, and allows the case of a bounded continuous cost function on a product of completely regular spaces to be treated directly, without the need to consider intermediate cases. Duality for a semicontinuous cost function is then deduced via the use of an...
On separation and approximation of real functions defined on a Choquet simplex
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