A note on a residual subset of Lispchitz functions on metric spaces

created by cavallett on 22 Oct 2013

[BibTeX]

Accepted Paper

Inserted: 22 oct 2013
Last Updated: 22 oct 2013

Journal: Proceedings of Edinburgh Math. Society
Year: 2013

Abstract:

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.