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POINTS OF $\varepsilon$-DIFFERENTIABILITY OF LIPSCHITZ FUNCTIONS FROM ${\bb R}^n$ TO ${\bb R}^{n-1}$

Published online by Cambridge University Press:  24 March 2003

THIERRY DE PAUW  and
PETRI HUOVINEN
THIERRY DE PAUW
Affiliation:
Université de Paris Sud, Equipe d'analyse harmonique, Bâtiment 425, F-91405 Orsay CEDEX, [email protected]
PETRI HUOVINEN
Affiliation:
University of Jyväskylä, Department of Mathematics, P.O. Box 35, FIN-40351 Jyväskylä, Finland [email protected]
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Abstract

This paper proves that for every Lipschitz function $f:{\bb R}^n\longrightarrow {\bb R}^m,\;m < n$ , there exists at least one point of $\varepsilon$ -differentiability of $f$ which is in the union of all $m$ -dimensional affine subspaces of the form $q_0+{\rm span}\{q_1,q_2,\ldots,q_m\},\;{\rm where}\;q_j(j=0,1,\ldots,m)$ are points in ${\bb R}^n$ with rational coordinates.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 5 , September 2002 , pp. 539 - 550
Copyright
© The London Mathematical Society 2002

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