Mathematical Notes

, Volume 64, Issue 1, pp 92–97 | Cite as

Concerning the possible values of upper and lower derivatives

  • G. G. Oniani


In this paper, the behavior of the upper and lower derivatives of integrals with respect to differential bases formed from intervals is studied. The main result consists in proving the fact that there are, in general, no analogs of the well-known Besicovitch theorem for translation-invariant Busemann-Feller bases formed from intervals.

Key words

upper and lower derivatives differential basis Besicovitch's theorem Busemann-Feller basis 


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  1. 1.
    A. S. Besicovitch, “On differentiation of Lebesgue double integrals,”Fund. Math.,25, 209–216 (1935).MATHGoogle Scholar
  2. 2.
    M. Gusman,Differentiation of Integrals inn Springer-Verlag, Heidelberg (1975).Google Scholar

Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • G. G. Oniani
    • 1
  1. 1.Tbilisi State UniversityUSSR

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