- Source: 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 Gδ set and a
G
δ
σ
{\displaystyle {G_{\delta }}_{\sigma }}
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", Rec. Math. (Mat. Sbornik), Nouvelle Série (in Russian and German), 9 (51): 487–510, MR 0004869.
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, MR 0022592.