Around Strassen's theorems

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 brie...

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Published inSbornik. Mathematics Vol. 216; no. 3; pp. 386 - 411
Main Authors Kusraev, Anatolii Georgievich, Kutateladze, Semen Samsonovich
Format Journal Article
LanguageEnglish
Published 2025
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Summary: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. Bibliography: 68 titles.
ISSN:1064-5616
1468-4802
DOI:10.4213/sm10200e