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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On the existence of regular approximate differentials


Author: Albert Fadell
Journal: Proc. Amer. Math. Soc. 37 (1973), 541-544
MSC: Primary 26A54
MathSciNet review: 0313462
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Abstract: We prove that for continuous real-valued functions on an open set in n-space, a sufficient condition for the existence a.e. of a regular approximate differential is that the functions have an ordinary total differential a.e. with respect to all but one variable.


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  • [1] R. Caccioppoli and G. Scorza Dragoni, Necessitá della condizione di Weierstrass per la semicontinuità di un integrale sopra una data superficie, Reale Acad. Ital. Mem. Cl. Sci. Fis. Math. Natur. 4 (1938), 251-268.
  • [2] Bruna Lodigiani, Sulla differenziabilità asintotica regolare delle funzioni di più variabili, Rend. Sem. Mat. Univ. Padova 22 (1953), 251–257 (Italian). MR 0057966 (15,299e)
  • [3] Hans Rademacher, Über partielle und totale differenzierbarkeit von Funktionen mehrerer Variabeln und über die Transformation der Doppelintegrale, Math. Ann. 79 (1919), no. 4, 340–359 (German). MR 1511935, http://dx.doi.org/10.1007/BF01498415
  • [4] T. Rado, On the derivative of the Lebesgue area of continuous surfaces, Fund. Math. 30 (1938), 34-39.
  • [5] -, On absolutely continuous transformations in the plane, Duke Math. J. 4 (1938), 219-220.
  • [6] S. Saks, Theory of the integral, 2nd ed., Monografie Mat., vol. 7, PWN, Warsaw, 1937.
  • [7] W. Stepanoff, Sur les conditions de l'existence de la différentielle totale, Mat. Sb. 32 (1925), 511-526.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0313462-9
PII: S 0002-9939(1973)0313462-9
Keywords: Regular approximate differential, total differential
Article copyright: © Copyright 1973 American Mathematical Society