A generalized dual maximizer for the Monge–Kantorovich transport problem
Mathias Beiglböck, Christian Léonard, Walter Schachermayer (2012)
ESAIM: Probability and Statistics
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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.