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 [math]\displaystyle{ {G_\delta}_\sigma }[/math] set of zero measure. This result was proved by Zygmunt Zahorski in 1939 and first published in 1941.

References

• Zahorski, Zygmunt (1941), "Punktmengen, in welchen eine stetige Funktion nicht differenzierbar ist" (in Russian, German), Rec. Math. (Mat. Sbornik), Nouvelle Série 9 (51): 487–510 .
• Zahorski, Zygmunt (1946), "Sur l'ensemble des points de non-dérivabilité d'une fonction continue" (French translation of 1941 Russian paper), Bulletin de la Société Mathématique de France 74: 147–178, doi:10.24033/bsmf.1381, http://www.numdam.org/numdam-bin/item?id=BSMF_1946__74__147_0 .