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

 

Integration by substitution


Author: Gerald S. Goodman
Journal: Proc. Amer. Math. Soc. 70 (1978), 89-91
MSC: Primary 26A39
MathSciNet review: 0476952
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0476952-9
PII: S 0002-9939(1978)0476952-9
Keywords: Integration by substitution, change of variables, chain rule, N-functions, Lebesgue integral, Denjoy integral, Perron integral
Article copyright: © Copyright 1978 American Mathematical Society