On the monotonicity of optimal transportation plans

[摘要] We obtain analytical properties of the maps that give optimal transportation plans for the L-2-Wasserstein distance. We take advantage of the monotonicity of such optimal transportation plans to discuss their measurability and continuity. As a main result of independent interest we obtain the a.e. continuity of monotone (in the sense of Zarantonello) operators. (C) 1997 Academic Press.

[发布日期] 1997-11-01