  This paper contains a very simple and general proof that eigenfunctions of
quantizations of classically ergodic systems become uniformly distributed in
phase space. This ergodicity property of eigenfunctions f is shown to follow
from a convexity inequality for the invariant states (Af,f). This proof of
ergodicity of eigenfunctions simplifies previous proofs (due to A.I.
Shnirelman, Colin de Verdiere and the author) and extends the result to the
much more general framework of C* dynamical systems.
