  In this paper we discuss the Mather problem for stationary Lagrangians, that
is Lagrangians $L:\Rr^n\times \Rr^n\times \Omega\to \Rr$, where $\Omega$ is a
compact metric space on which $\Rr^n$ acts through an action which leaves $L$
invariant. This setting allow us to generalize the standard Mather problem for
quasi-periodic and almost-periodic Lagrangians. Our main result is the
existence of stationary Mather measures invariant under the Euler-Lagrange flow
which are supported in a graph. We also obtain several estimates for viscosity
solutions of Hamilton-Jacobi equations for the discounted cost infinite horizon
problem.
