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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the existence of regular approximate differentials
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by Albert Fadell PDF
Proc. Amer. Math. Soc. 37 (1973), 541-544 Request permission

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.
References
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  • Bruna Lodigiani, Sulla differenziabilità asintotica regolare delle funzioni di più variabili, Rend. Sem. Mat. Univ. Padova 22 (1953), 251–257 (Italian). MR 57966
  • 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, DOI 10.1007/BF01498415
  • T. Rado, On the derivative of the Lebesgue area of continuous surfaces, Fund. Math. 30 (1938), 34-39. —, On absolutely continuous transformations in the plane, Duke Math. J. 4 (1938), 219-220. S. Saks, Theory of the integral, 2nd ed., Monografie Mat., vol. 7, PWN, Warsaw, 1937. W. Stepanoff, Sur les conditions de l’existence de la différentielle totale, Mat. Sb. 32 (1925), 511-526.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 37 (1973), 541-544
  • MSC: Primary 26A54
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0313462-9
  • MathSciNet review: 0313462