Real Analysis Exchange

Approximations by Lipschitz functions generated by extensions.

Radu Miculescu

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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 $X$.

Article information

Real Anal. Exchange, Volume 28, Number 1 (2002), 33-41.

First available in Project Euclid: 12 June 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A16: Lipschitz (Hölder) classes 41A99: None of the above, but in this section

Lipschitz functions approximation extension


Miculescu, Radu. Approximations by Lipschitz functions generated by extensions. Real Anal. Exchange 28 (2002), no. 1, 33--41.

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