Around Strassen's theorems | Sciact

Around Strassen's theorems Full article

Journal

Sbornik Mathematics
ISSN: 1064-5616 , E-ISSN: 1468-4802

Output data

Year: 2025, Volume: 216, Number: 3, Pages: 386-411 Pages count : 27 DOI: 10.4213/sm10200e

Tags

Strassen theorems, disintegration, subdifferential, duality, Monge–Kantorovich problem, Choquet theory.

Authors

Kusraev Anatolii Georgievich ¹ , Kutateladze Semen Samsonovich ²

Affiliations

1	North Caucasus Center for Mathematical Research, Vladikavkaz Scientific Centre of the Russian Academy of Sciences, Vladikavkaz, Russia
2	Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Funding (2)

1	Sobolev Institute of Mathematics	FWNF-2022-0004
2	Министерство науки и высшего образования РФ	075-02-2024-1379

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 HahnBanach–Kantorovich theorem, the intrinsic characterization of subdifferentials, the Radon–Nikod´ ym theorem for positive operators, measurable Banach bundles with lifting, Maharam extension and the tensor product of vector lattices, is given.

Kusraev A.G. , Kutateladze S.S.
Around Strassen's theorems
Sbornik Mathematics. 2025. V.216. N3. P.386-411. DOI: 10.4213/sm10200e WOS Scopus OpenAlex

Кусраев А.Г. , Кутателадзе С.С.
Вокруг теорем Штрассена
Математический сборник. 2025. Т.216. №3. С.128–155. DOI: 10.4213/sm10200 РИНЦ OpenAlex

Submitted:	Sep 17, 2024
Published print:	May 19, 2025
Published online:	May 19, 2025

Web of science:	WOS:001497528100009
Scopus:	2-s2.0-105006983818
OpenAlex:	W4410385158

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