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...