Real Analysis Exchange

A Simple Proof of Zahorski’s Description of Non-Differentiability Sets of Lipschitz Functions

Thomas Fowler and David Preiss

Full-text: Open access

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 $G$.

Article information

Source
Real Anal. Exchange Volume 34, Number 1 (2008), 127-138.

Dates
First available: 19 May 2009

Permanent link to this document
http://projecteuclid.org/euclid.rae/1242738925

Mathematical Reviews number (MathSciNet)
MR2527127

Zentralblatt MATH identifier
1179.26010

Subjects
Primary: 26A27: Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives

Keywords
Lipschitz functions sets of non-differentiability

Citation

Fowler, Thomas; Preiss, David. A Simple Proof of Zahorski’s Description of Non-Differentiability Sets of Lipschitz Functions. Real Analysis Exchange 34 (2008), no. 1, 127--138. http://projecteuclid.org/euclid.rae/1242738925.


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References

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  • G. Piranian,The set of non-differentiability of a continuous function, Amer. Math. Monthly 73(4) (1966), no. 4, 57–61.
  • Z. Zahorski, Sur l'ensemble des points de non-dérivabilité d'une fonction continue, Bull. Soc. Math. France 74 (1946), 147–178.