A generalized dual maximizer for the Monge–Kantorovich transport problem
نویسندگان
چکیده
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.
منابع مشابه
An Introduction to the Mass Transportation Theory and its Applications
2 Formulation of the mass transport problems 4 2.1 The original Monge-Kantorovich problem . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Guessing a good dual to the Monge-Kantorovich problem . . . . . . . . . . . . . 6 2.3 Properties of ”Extreme points of C” . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Existence of a minimizer . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
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