Illinois Journal of Mathematics

Definable smoothing of Lipschitz continuous functions

Andreas Fischer

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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.

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

First available in Project Euclid: 23 July 2009

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Zentralblatt MATH identifier

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


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

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