Abstract:
Two famous theorems of Strassen, on disintegration and the existence of a probability measure with given marginals, are extended to the case of operators in Kantorovich spaces. Relations of Strassen's theorems to the Monge–Kantorovich problem and Choquet's theory are also indicated. A brief survey of the necessary machinery, namely, the Hahn–Banach–Kantorovich theorem, the intrinsic characterization of subdifferentials, the Radon–Nikodým theorem for positive operators, measurable Banach bundles with lifting, Maharam extension and the tensor product of vector lattices, is given.
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