  Let (X, d) be a quasi-convex, complete and separable metric space with
reference probability measure m. We prove that the set of of real valued
Lipschitz function with non zero point-wise Lipschitz constant m-almost
everywhere is residual, and hence dense, in the Banach space of Lipschitz and
bounded functions. The result is the metric analogous of a result proved for
real valued Lipschitz maps defined on R2 by Alberti, Bianchini and Crippa in
[1].

Analysis of PDEs;Metric Geometry