Real Analysis Exchange

The Primitive of a Kurzweil-Henstock Integrable Function in Multidimensional Space

Emmanuel Cabral and Lee Peng-Yee

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Abstract

In this paper, give a new, full characterization of the primitive of a Kurzweil-Henstock integrable function in multidimensional space.

Article information

Source
Real Anal. Exchange, Volume 27, Number 2 (2001), 627-634.

Dates
First available in Project Euclid: 2 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1212412860

Mathematical Reviews number (MathSciNet)
MR1922673

Zentralblatt MATH identifier
1069.26013

Subjects
Primary: 26A39: Denjoy and Perron integrals, other special integrals

Keywords
Kurzweil-Henstock integrable function primitive full characterization

Citation

Cabral, Emmanuel; Peng-Yee, Lee. The Primitive of a Kurzweil-Henstock Integrable Function in Multidimensional Space. Real Anal. Exchange 27 (2001), no. 2, 627--634. https://projecteuclid.org/euclid.rae/1212412860


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References

  • Cabral, E.A. and Lee, P.Y., A Fundamental Theorem of Calculus for the Kurzweil-Henstock Integral in $ \mathbb{R}^{m}$, Real Analysis Exchange, 26(2001-2002), 867-876.
    Mathematical Reviews (MathSciNet): MR1844400
    Zentralblatt MATH: 1024.26005
    Project Euclid: euclid.rae/1214571374
  • de Guzman, M. Differentiation of Integrals in $\mathbb{R}^{n}$, Springer-Verlag, Berlin, 1976.
  • Folland, G.B., Real Analysis: Modern Techniques and Applications, Second Edition, John Wiley and Sons Inc., U.S.A., 1999.
    Mathematical Reviews (MathSciNet): MR1681462
  • Gordon, R.A., The Integrals of Lebesgue, Denjoy, Perron and Henstock, Graduate Studies in Mathematics, Volume 4, American Mathematical Society, 1994.
    Mathematical Reviews (MathSciNet): MR1288751
    Zentralblatt MATH: 0807.26004
  • Lee, P.Y., Lanzhou Lectures on Henstock Integration, World Scientific Publishing Co., Singapore, 1989.
    Mathematical Reviews (MathSciNet): MR1050957
    Zentralblatt MATH: 0699.26004
  • Lu, J. T. and Lee, P.Y., The Primitives of Henstock Integrable Functions in Euclidean Space, Bull.

Michigan State University Press

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