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On some classical measure-theoretic theorems for non-sigma-complete Boolean algebras

CONTENTSIntroduction...................................................................................5§1. Preliminaries...........................................................................7§2. Definitions and a theorem of Diestel, Faires and Huff.............9§3. Examples...............................................................................13§4. Some special classes of Boolean algebras ..........................19§5. The Grothendieck property...................................................22§6....

A generalized dual maximizer for the Monge–Kantorovich transport problem

Mathias BeiglböckChristian LéonardWalter Schachermayer — 2012

ESAIM: Probability and Statistics

The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces are assumed to be polish and equipped with Borel probability measures and . The transport cost function :  ×  →  [0,∞]  is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic and rely on Fenchel’s perturbation technique.

A general duality theorem for the Monge-Kantorovich transport problem

Mathias BeiglböckChristian LéonardWalter Schachermayer — 2012

Studia Mathematica

The duality theory for the Monge-Kantorovich transport problem is analyzed in a general setting. The spaces X,Y are assumed to be Polish and equipped with Borel probability measures μ and ν. The transport cost function c: X × Y → [0,∞] is assumed to be Borel. Our main result states that in this setting there is no duality gap provided the optimal transport problem is formulated in a suitably relaxed way. The relaxed transport problem is defined as the limiting cost of the partial transport...

A generalized dual maximizer for the Monge–Kantorovich transport problem

Mathias BeiglböckChristian LéonardWalter Schachermayer — 2012

ESAIM: Probability and Statistics

The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces are assumed to be polish and equipped with Borel probability measures and . The transport cost function :  ×  →  [0,∞]  is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic and rely...

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