J. Schmeling and S. Troubetzkoy Scaling Properties of Hyperbolic Measures (100K, Dvi) ABSTRACT. In this article we consider a class of maps which includes $C^{1 + \alpha}$ diffeomorphisms as well as invertible and nonivertible maps with piecewise smooth singularities. We prove a general scaling result for any hyperbolic measure which is invariant for a map from our class. The existence of the pointwise dimension and the Brin-Katok local entropy formula are special cases of our scaling result.