  We prove that $c$-cyclically monotone transport plans $\pi$ 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.
