Displaying similar documents to “A simple proof in Monge-Kantorovich duality theory”

A general duality theorem for the Monge-Kantorovich transport problem

Mathias Beiglböck, Christian Léonard, Walter Schachermayer (2012)

Studia Mathematica

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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...

A decomposition of complex Monge-Ampère measures

Yang Xing (2007)

Annales Polonici Mathematici

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We prove a decomposition theorem for complex Monge-Ampère measures of plurisubharmonic functions in connection with their pluripolar sets.

Monge-Ampère boundary measures

Urban Cegrell, Berit Kemppe (2009)

Annales Polonici Mathematici

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We study swept-out Monge-Ampère measures of plurisubharmonic functions and boundary values related to those measures.

Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals

S. T. Rachev, R. M.

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CONTENTS§0. Introduction...................................................................................................................................5§1. Notation and terminology..............................................................................................................6§2. A generalization of the Kantorovich-Rubinstein theorem..............................................................8§3. Application: explicit representations for a class of probability metrics.........................................14§4....