## Real Analysis Exchange

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

#### 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 in Project Euclid: 19 May 2009

http://projecteuclid.org/euclid.rae/1242738925

Mathematical Reviews number (MathSciNet)
MR2527127

Zentralblatt MATH identifier
1179.26010

#### Citation

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

#### References

• A. M. Bruckner, Differentiation of Real Functions, Lecture Notes in Math. 659 (1978), Springer-Verlag.
• J. Lukeš, J. Malý and L. Zajíček, Fine Topology Methods in Real Analysis and Potential Theory, Lecture Notes in Math. 1189 (1986), Springer-Verlag.
• 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.