Smoothness of functions with respect to a set

V. A. Startsev

Daugavpils Pedagogical Institute, USSR

Abstract: In this note we consider the properties of functions which are smooth with respect to congruent sets. We find necessary and sufficient conditions which these congruent sets must satisfy in order that asymptotic differentiability, together with the smoothness relative to a set, will imply ordinary differentiability almost everywhere. We consider the case of measurable and continuous functions.

UDC: 517.9

Received: 06.10.1972

 English version: Mathematical Notes, 1974, 15:3, 251–254

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