In this note we derive an upper bound for the Hausdorff and box
dimension of the stable and local stable set of a hyperbolic set
$\Lambda$ of a $C^2$ diffeomorphisms on a $n$-dimensional manifold.
As a consequence we obtain that dim$_H W^s(\Lambda)=n$ is equivalent
to the existence of a SRB-measure. We also discuss related
results for expanding maps.