Zahorski theorem

In mathematics, Zahorski's theorem is a theorem of real analysis. It states that a necessary and sufficient condition for a subset of the real line to be the set of points of non-differentiability of a continuous real-valued function, is that it be the union of a G_δ set and a $${G_delta}_sigma set of zero measure.

This result was proved by Zygmunt Zahorski in 1939 and first published in 1941.

References

* [http://archive.numdam.org/article/BSMF_1946__74__147_0.pdf Sur l'ensemble des points de non-derivabilite d'une fonction continue] , Zygmunt Zahorski, Bulletin de la Société Mathématique de France 74 (1946), p. 147-178