Beiglböck, Mathias; Léonard, Christian; Schachermayer, Walter
A generalized dual maximizer for the Monge-Kantorovich transport problem
ESAIM: Probability and Statistics, Tome 16 (2012) , p. 306-323
Zbl 1263.49057 | MR 2956577
doi : 10.1051/ps/2011163
URL stable : http://www.numdam.org/item?id=PS_2012__16__306_0

Classification:  46E30,  46N10,  49J45,  28A35
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.

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