A generalized dual maximizer for the Monge-Kantorovich transport problem
ESAIM: Probability and Statistics, Volume 16 (2012), pp. 306-323.

The dual attainment of 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 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.

DOI: 10.1051/ps/2011163
Classification: 46E30, 46N10, 49J45, 28A35
Keywords: optimal transport, duality in function spaces, Fenchel's perturbation technique
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Beiglböck, Mathias; Léonard, Christian; Schachermayer, Walter. A generalized dual maximizer for the Monge-Kantorovich transport problem. ESAIM: Probability and Statistics, Volume 16 (2012), pp. 306-323. doi : 10.1051/ps/2011163. http://archive.numdam.org/articles/10.1051/ps/2011163/

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