  We show that for any C^1+alpha diffeomorphism of a compact Riemannian
manifold, every non-atomic, ergodic, invariant probability measure with
non-zero Lyapunov exponents is approximated by uniformly hyperbolic sets in the
sense that there exists a sequence Omega_n of compact, topologically
transitive, locally maximal, uniformly hyperbolic sets, such that for any
sequence mu_n of f-invariant ergodic probability measures with supp (mu_n) in
Omega_n we have mu_n -> mu in the weak-* topology.
