A Simple Proof of Zahorski’s Description of Non-Differentiability Sets of Lipschitz Functions
Thomas Fowler and David Preiss
Source: Real Anal. Exchange Volume 34, Number 1
(2008), 127-138.
Abstract
We provide a simplification of Zahorski's argument showing that for every Lebesgue null $G_{\delta\sigma}$ subset $G$ of the line there is a Lipschitz function that is non-differentiable precisely at the points of $G$.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.rae/1242738925
Mathematical Reviews number (MathSciNet): MR2527127
Zentralblatt MATH identifier: 1179.26010
References
A. M. Bruckner, Differentiation of Real Functions, Lecture Notes in Math. 659 (1978), Springer-Verlag.
Mathematical Reviews (MathSciNet): MR507448
J. Lukeš, J. Malý and L. Zajíček, Fine Topology Methods in Real Analysis and Potential Theory, Lecture Notes in Math. 1189 (1986), Springer-Verlag.
Mathematical Reviews (MathSciNet): MR861411
G. Piranian,The set of non-differentiability of a continuous function, Amer. Math. Monthly 73(4) (1966), no. 4, 57–61.
Mathematical Reviews (MathSciNet): MR193193
Digital Object Identifier: doi:10.2307/2313750
Z. Zahorski, Sur l'ensemble des points de non-dérivabilité d'une fonction continue, Bull. Soc. Math. France 74 (1946), 147–178.
Mathematical Reviews (MathSciNet): MR22592
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