A generalized dual maximizer for the Monge–Kantorovich transport problem
A generalized dual maximizer for the Monge–Kantorovich transport problem
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 …