Illinois Journal of Mathematics

Definable smoothing of Lipschitz continuous functions

Andreas Fischer

Full-text: Open access

Abstract

Let $\mathcal M$ be an $o$-minimal expansion of a real closed field. We prove the definable smoothing of definable Lipschitz continuous functions. In the case of Lipschitz functions of one variable, we are even able to preserve the Lipschitz constant.

Article information

Source
Illinois J. Math., Volume 52, Number 2 (2008), 583-590.

Dates
First available in Project Euclid: 23 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1248355351

Digital Object Identifier
doi:10.1215/ijm/1248355351

Mathematical Reviews number (MathSciNet)
MR2524653

Zentralblatt MATH identifier
1193.03064

Subjects
Primary: 03C64: Model theory of ordered structures; o-minimality

Citation

Fischer, Andreas. Definable smoothing of Lipschitz continuous functions. Illinois J. Math. 52 (2008), no. 2, 583--590. doi:10.1215/ijm/1248355351. https://projecteuclid.org/euclid.ijm/1248355351


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