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On differentiability of real functions

  • Santi Valenti
Article
  • 14 Downloads

Summary

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.

Keywords

Lebesgue Measure Relative Weight English Translation Real Function Algebraic Variation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Baire R.,Leçons sur les Théories Générales de l’Analyse, Gauthier-Villars, Paris (1907).MATHGoogle Scholar
  2. [2]
    Hartman S.—Mikusiński J.,The Theory of Lebesgue Measure and Integration, Państwowe Wydawnictwo Naukowe, Warszawa (1961), (English translation).MATHGoogle Scholar
  3. [3]
    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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