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2002-2003 Approximations by Lipschitz functions generated by extensions.
Radu Miculescu
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Real Anal. Exchange 28(1): 33-41 (2002-2003).


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 $X$.


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Radu Miculescu. "Approximations by Lipschitz functions generated by extensions.." Real Anal. Exchange 28 (1) 33 - 41, 2002-2003.


Published: 2002-2003
First available in Project Euclid: 12 June 2006

zbMATH: 1074.41013
MathSciNet: MR1973966

Primary: 26A16 , 41A99

Keywords: approximation , Extension‎ , Lipschitz functions

Rights: Copyright © 2002 Michigan State University Press

Vol.28 • No. 1 • 2002-2003
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