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On differentiability of real functions

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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.

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References

  1. Baire R.,Leçons sur les Théories Générales de l’Analyse, Gauthier-Villars, Paris (1907).

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  2. Hartman S.—Mikusiński J.,The Theory of Lebesgue Measure and Integration, Państwowe Wydawnictwo Naukowe, Warszawa (1961), (English translation).

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  3. Pettineo B.,Sulla derivabilità delle funzioni, Atti Acc. Naz. Lincei (Memorie), s. VIII, v. VII, f. 6 (1965).

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Authors and Affiliations

  1. Palermo

    Santi Valenti

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  1. Santi Valenti
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Lavoro eseguito nell’ambito dell’attività dei Raggruppamenti di Ricerca del Comitato per le Scienze Matematiche del C.N.R.

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Valenti, S. On differentiability of real functions. Rend. Circ. Mat. Palermo 19, 5–10 (1970). https://doi.org/10.1007/BF02843884

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  • DOI: https://doi.org/10.1007/BF02843884

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