  Gomes and Valdinoci have introduced a time-step approximation scheme for a
viscous version of Aubry-Mather theory; this scheme is a variant of that of
Jordan, Kinderlehrer and Otto. Gangbo and Tudorascu have shown that the Vlasov
equation can be seen as an extension of Aubry-Mather theory, in which the
configuration space is the space of probability measures, i. e. the different
distributions of infinitely many particles on a manifold. Putting the two
things together, we show that Gomes and Valdinoci's theorem carries over to a
viscous version of the Vlasov equation. In this way, we shall recover a theorem
of J. Feng and T. Nguyen, but by a different and more "elementary" proof.
