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The Vlasov equation models the motion of a group of particles on a manifold,say the pdimensional torus,which are governed by an external potential and a mutual interaction.Recently,W.Gangbo and A.Tudorascu extended Aubry-Mather theory to this setting; we shall briefly review their results and show how the viscous Aubry-Mather theory of D.Gomes fits into this setting.