Real Analysis Exchange

Notes on the approximately continuous Henstock integral

Shipan Lu

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Abstract

There are two different definitions about the approximately continuous Henstock integral or \(AH\) integral, for short. In this paper we prove that they are equivalent, and that the \(AH\) integral is included in the \(AD\) integral defined by Kubota in 1964. Also we give a solution for the problem put forward by Gordon (1994, p. 255).

Article information

Source
Real Anal. Exchange, Volume 22, Number 1 (1996), 377-381.

Dates
First available in Project Euclid: 1 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1338515229

Mathematical Reviews number (MathSciNet)
MR1433622

Zentralblatt MATH identifier
0879.26035

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

Keywords
AH integral AD integral

Citation

Lu, Shipan. Notes on the approximately continuous Henstock integral. Real Anal. Exchange 22 (1996), no. 1, 377--381. https://projecteuclid.org/euclid.rae/1338515229


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References

  • S. Fu, S-Henstock integration and the approximately strong Lusin condition, Real Anal. Exchange 19 (1993-1994), 312–316.
  • R. Gordon, The inversion of approximate and dyadic derivatives using an extension of the Henstock integral, Real Anal. Exchange 16 (1990-1991), 154–168.
  • R. Gordon, The integrals of Lebesgue, Denjoy, Perron and Henstock, AMS (1994).
  • Y. Kubota, An integral of Denjoy type, Proc. Japan Acad 40 (1964), 713–717.
  • S. Saks, Theory of the integral, 2nd. rev. ed., vol. PWN, Monografie Matematyczne, Warsaw, 1937.