2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141717We prove that $c$-cyclically monotone transport plans $π$ optimize the Monge-Kantorovich transportation problem under an additional measurability condition. This measurability condition is always satisfied for finitely valued, lower semi-continuous cost functions. In particular, this yields a positive answer to Problem 2.25 in C. Villani's book. We emphasize that we do not need any regularity conditions as were imposed in the previous literature.to appear in Proceedings of the AMSOptimization and ControlFunctional Analysis49J45,28A35text