Abstract
We consider the Monge-Kantorovich transport problem in an abstract measure theoretic setting. Our main result states that duality holds if c: X x Y → [0, ∞) is an arbitrary Borel measurable cost function on the product of Polish spaces X, Y. In the course of the proof we show how to relate a non-optimal transport plan to the optimal transport costs via a subsidy function and how to identify the dual optimizer. We also provide some examples showing the limitations of the duality relations.
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