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2000/2001 Approximation of Continuous Functions by Lipschitz Functions
Radu Miculescu
Real Anal. Exchange 26(1): 449-452 (2000/2001).


Georganopoulos (see [1] ) has shown that a continuous function $% f:X\rightarrow B$, where $X$ is a compact metric space and $B$ a convex subset of a real normed space $Y$, is the uniform limit of a sequence of Lipschitz maps from $X$ to $B$. In this note we obtain a similar result, namely we show that a continuous function $f:X\rightarrow R$, where $X$ is a metric space, is a uniform limit of a sequence of locally Lipschitz maps from $X$ to $R$. When $X$ is compact and $B=Y=R$, we get the Georganopoulos's result.


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Radu Miculescu. "Approximation of Continuous Functions by Lipschitz Functions." Real Anal. Exchange 26 (1) 449 - 452, 2000/2001.


Published: 2000/2001
First available in Project Euclid: 2 January 2009

zbMATH: 1010.26004
MathSciNet: MR1825525

Primary: 26A16 , 32 , ‎54C30 , 70

Keywords: approximation , Continuous function , Lipschitz functions

Rights: Copyright © 2000 Michigan State University Press

Vol.26 • No. 1 • 2000/2001
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