DUALITY FOR BOREL MEASURABLE COST FUNCTIONS

作者：Beiglboeck Mathias; Schachermayer Walter

来源：Transactions of the American Mathematical Society, 2011, 363(8): 4203-4224.

DOI：10.1090/S0002-9947-2011-05174-3

• Monge-Kantorovich problem
• Monge-Kantorovich duality
• c-cyclical monotonicity
• measurable cost function

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, infinity) 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.

• 出版日期2011-8