Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Integration by substitution
HTML articles powered by AMS MathViewer

by Gerald S. Goodman PDF
Proc. Amer. Math. Soc. 70 (1978), 89-91 Request permission

Abstract:

The author shows how N-functions provide a natural setting in which to establish the change of variables formula for Lebesgue or Denjoy/Perron integrals. By abolishing the need to pass to the limit under the integral sign, the validity of the classical formula is significantly extended, yielding new results even in the case of Lebesgue integrals.
References
    S. Banach, Sur une classe de fonctions continues, Fund. Math. 8 (1926), 166-172.
  • Nina Bary, Mémoire sur la représentation finie des fonctions continues, Math. Ann. 103 (1930), no. 1, 185–248 (French). MR 1512621, DOI 10.1007/BF01455694
  • Gerald S. Goodman, $N$-functions and integration by substitution, Rend. Sem. Mat. Fis. Milano 47 (1977), 123–134 (1979) (English, with Italian summary). MR 526879, DOI 10.1007/BF02925747
  • Edward James McShane, Integration, Princeton University Press, Princeton, N. J., 1944 1957. MR 0082536
    • S. Saks, Sur certaines classes de fonctions continues, Fund. Math. 17 (1931), 124-151. —, Theory of the integral, Monogr. Mat., vol. 7, PWN, Warsaw, 1937.
  • James Serrin and Dale E. Varberg, A general chain rule for derivatives and the change of variables formula for the Lebesgue integral, Amer. Math. Monthly 76 (1969), 514–520. MR 247011, DOI 10.2307/2316959
  • G. P. Tolstov, On the curvilinear and iterated integral, Trudy Mat. Inst. Steklov. 35 (1950), 102 (Russian). MR 0044612
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26A39
  • Retrieve articles in all journals with MSC: 26A39
Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 70 (1978), 89-91
  • MSC: Primary 26A39
  • DOI: https://doi.org/10.1090/S0002-9939-1978-0476952-9
  • MathSciNet review: 0476952