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

Uniform hyperbolic approximations of measures with non zero Lyapunov exponents