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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-delta set|G<sub>&delta;</sub> set]] and a <math>{G_\delta}_\sigma</math> set of [[zero measure]].

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

==References==
*{{citation|first=Zygmunt|last=Zahorski|title=Punktmengen, in welchen eine stetige Funktion nicht differenzierbar ist|format=Russian with German summary|journal=Rec. Math. (Mat. Sbornik) N.S.|volume=9|issue=51|year=1941|pages=487–510|mr=0004869}}.
*{{citation|url=http://www.numdam.org/numdam-bin/item?id=BSMF_1946__74__147_0|title=Sur l'ensemble des points de non-dérivabilité d'une fonction continue|first=Zygmunt|last=Zahorski|journal=Bulletin de la Société Mathématique de France|volume=74|year=1946|pages=147–178|mr=0022592|format=French translation of 1941 Russian paper}}.

[[Category:Real analysis]]
[[Category:Theorems in analysis]]


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