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We consider the Riemannian universal covering of a compact manifold $M = X /\Gamma$ and assume that $\Gamma$ is amenable. We show for an ergodic randomfamily of Schr\"odinger operators on $X$ the existence of a (non-random)integrated density of states.Comment: LaTeX 2e, amsart, 17 pages; appeared in a somewhat different form in  Geometriae Dedicata, 91 (1): 117-135, (2002

Integrated density of states for ergodic random Schrödinger operators on manifolds