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 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.
Authors
- S. S. Kutateladze (ORCID: https://orcid.org/0000-0002-5306-2788)
- A.G. Kusraev
Institutions
- Sobolev Institute of Mathematics (RU)
- Siberian Branch of the Russian Academy of Sciences (RU)
- Federal State Budgetary Institution of Science Federal Scientific Center "Vladikavkaz Scientific Center of the Russian Academy of Sciences" (RU)
Publication Details
- Journal
- Sbornik Mathematics
- Published
- 2025-01-01
- DOI
- https://doi.org/10.4213/sm10200e
- Primary Topic
- Advanced Banach Space Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Centre de Recherches Mathématiques
- Ministry of Education and Science of the Russian Federation
- Ministry of Science and Higher Education of the Russian Federation
- Russian Academy of Sciences
- Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences