On differentiability of real functions

  • Santi Valenti


In this paper a necessary and sufficient condition, in order that a (real-valued) function of a real variable,-defined on an interval (a, b)-, be differentiable almost everywhere in this interval, is given.

The peculiarity of the condition is that of involving only a subset Z of (a, b) dense on (a, b), but of measure 0.


Lebesgue Measure Relative Weight English Translation Real Function Algebraic Variation 
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    Baire R.,Leçons sur les Théories Générales de l’Analyse, Gauthier-Villars, Paris (1907).MATHGoogle Scholar
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    Hartman S.—Mikusiński J.,The Theory of Lebesgue Measure and Integration, Państwowe Wydawnictwo Naukowe, Warszawa (1961), (English translation).MATHGoogle Scholar
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    Pettineo B.,Sulla derivabilità delle funzioni, Atti Acc. Naz. Lincei (Memorie), s. VIII, v. VII, f. 6 (1965).Google Scholar

Copyright information

© Springer 1970

Authors and Affiliations

  • Santi Valenti
    • 1
  1. 1.Palermo

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