Real Analysis Exchange

On Singularity of Henstock Integrable Functions

Peng-Yee Lee and Jitan Lu

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Abstract

We define a singular point of a Henstock integrable function to be one which is not contained in any open interval on which the function is Lebesgue integrable. Then we give examples to illustrate the possible measure of the set of such singular points.

Article information

Source
Real Anal. Exchange, Volume 25, Number 2 (1999), 795-798.

Dates
First available in Project Euclid: 3 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.rae/1230995414

Mathematical Reviews number (MathSciNet)
MR1778532

Zentralblatt MATH identifier
1015.26016

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

Keywords
Singular point; Henstock integrable function; Lebesgue integrable function

Citation

Lee, Peng-Yee; Lu, Jitan. On Singularity of Henstock Integrable Functions. Real Anal. Exchange 25 (1999), no. 2, 795--798. https://projecteuclid.org/euclid.rae/1230995414


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References

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  • G. B. Folland, Real analysis, modern techniques and their applications, New York, 1984.
  • P. Y. Lee, Lanzhou lectures on Henstock integral, World Scientific, 1989.
  • S. Saks, Theory of the integral, New York, 1937.