  Let $f$ be a $C^{1+\alpha}$ diffeomorphism of a compact Riemannian manifold
and $\mu$ an ergodic hyperbolic measure with positive entropy. We prove that
for every continuous potential $\phi$ there exists a sequence of basic sets
$\Omega_n$ such that the topological pressure $P(f|\Omega_n,\phi)$ converges to
the free energy $P_{\mu}(\phi) = h(\mu) + \int\phi{d\mu}$. Then we introduce a
class of potentials $\phi$ for which there exists sequence of basic sets
$\Omega_n$ such that $P(f|\Omega_n,\phi) \to P(\phi)$.
