Real Analysis Exchange

A change of variables theorem for the Riemann integral

D. N. Sarkhel and Rudolf Výborný

Full-text: Open access

Abstract

The change of variables formula for the Riemann integral is discussed and a theorem is proved which perhaps compares favorably with its counterpart in Lebesgue theory.

Article information

Source
Real Anal. Exchange, Volume 22, Number 1 (1996), 390-395.

Dates
First available in Project Euclid: 1 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1338515231

Mathematical Reviews number (MathSciNet)
MR1433624

Zentralblatt MATH identifier
0879.26036

Subjects
Primary: 26A39: Denjoy and Perron integrals, other special integrals 26A42: Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX]

Keywords
Riemann integration substitution

Citation

Sarkhel, D. N.; Výborný, Rudolf. A change of variables theorem for the Riemann integral. Real Anal. Exchange 22 (1996), no. 1, 390--395. https://projecteuclid.org/euclid.rae/1338515231


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References

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  • E. W. Hobson, The Theory of Functions $\dots$, Vol. 1, Dover, New York.
  • K. Krzyżewski, On change of variable in the Denjoy-Perron integral I, Coll. Math, 9 (1962), 99–104.
  • K. Krzyżewski, On change of variable in the Denjoy-Perron integral II, Coll. Math, 9 (1962), 317–323.
  • J. Serrin and D. E. Varberg, A General Chain Rule for Derivatives and Change of Variables Formula for the Lebesgue Integral, The American Mathematical Monthly, 76 (1969), 514–520.
  • de la Valée Poussin, Sur l'intégrale de Lebesgue, Trans. Amer. Math. Soc., 16 (1915), 435–501.