Geodesic
Around Strassen's theorems
Sbornik. Mathematics, Tome 216 (2025) no. 3, pp. 386-411

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: Strassen theorems, disintegration, subdifferential, duality, Monge–Kantorovich problem, Choquet theory. 
@article{SM_2025_216_3_a8,
     author = {A. G. Kusraev and S. S. Kutateladze},
     title = {Around {Strassen's} theorems},
     journal = {Sbornik. Mathematics},
     pages = {386--411},
     publisher = {mathdoc},
     volume = {216},
     number = {3},
     year = {2025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2025_216_3_a8/}
}
TY  - JOUR
AU  - A. G. Kusraev
AU  - S. S. Kutateladze
TI  - Around Strassen's theorems
JO  - Sbornik. Mathematics
PY  - 2025
SP  - 386
EP  - 411
VL  - 216
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2025_216_3_a8/
LA  - en
ID  - SM_2025_216_3_a8
ER  - 
%0 Journal Article
%A A. G. Kusraev
%A S. S. Kutateladze
%T Around Strassen's theorems
%J Sbornik. Mathematics
%D 2025
%P 386-411
%V 216
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2025_216_3_a8/
%G en
%F SM_2025_216_3_a8
A. G. Kusraev; S. S. Kutateladze. Around Strassen's theorems. Sbornik. Mathematics, Tome 216 (2025) no. 3, pp. 386-411. http://geodesic.mathdoc.fr/item/SM_2025_216_3_a8/