Approximations by Lipschitz functions generated by extensions.

Miculescu, Radu

Real Anal. Exchange, Tome 28 (2002) no. 1, p. 33-41 / Harvested from Project Euclid

Résumé

We show that, for each pair of metric spaces that has the Lipschitz extension property, every bounded uniformly continuous function can be approximated by Lipschitz functions. The same statement is valid for functions between a locally convex space and $\mathbb{R}^{n}$. In addition, we show that for a locally bounded, convex function $F:X\rightarrow\mathbb{R}^{n}$, where $X$ is a separable Fréchet space, the set of points on which the differential of this function exists is dense in $X$.

Détail

Publié le : 2002-05-14
Classification:  Lipschitz functions,  approximation,  extension,  26A16,  41A99