Rendiconti del Circolo Matematico di Palermo

, Volume 28, Issue 1, pp 33–36 | Cite as

Un teorema sulla rappresentazione degli integrali

  • Benedetto Bongiorno
  • Pasquale Vetro


be a De Possel differentiation basis in a complete measure space
, with μ≥0, μ(X)<+∞; letB be a Banach space and
When the
F′ exists μ-a.e. onX, we prove that for eachp>0, the μ-integral of‖F′‖ p is the lower-bound of a class ofp-variations.


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  1. [1]
    Bongiorno B.,Differentiation of set functions, Rend. Circ. Mat. Palermo,26 (1977), 37–51.MATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    Bongiorno B.—Vetro P.,Su un teorema di F. Riesz, Atti Accad. Sci. Lett. Arti Palermo, (4)37 (1977-78) parte I, 3–13.MathSciNetGoogle Scholar
  3. [3]
    Riesz F.—Sz-Nagy B.,Leçons d'Analyse Fonctionelle, 2me edition, Akademiai Kiado, Budapest, 1953.Google Scholar
  4. [4]
    Tonelli L.,Sul differenziale dell'arco di curva, Rend. Accad. Lincei,25 (1916), 207–213.Google Scholar

Copyright information

© Springer 1979

Authors and Affiliations

  • Benedetto Bongiorno
    • 1
  • Pasquale Vetro
    • 1
  1. 1.Instituto di MatematicaPalermo

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