Real Analysis Exchange

On Singularity of Henstock Integrable Functions

Peng-Yee Lee and Jitan Lu

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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

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

First available in Project Euclid: 3 January 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Singular point; Henstock integrable function; Lebesgue integrable function


Lee, Peng-Yee; Lu, Jitan. On Singularity of Henstock Integrable Functions. Real Anal. Exchange 25 (1999), no. 2, 795--798.

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  • Z. Buczolich, Henstock integrable functions are Lebesgue integrable on a portion, Proc. Amer. Math. Soc., 111(1991), 127–129.
  • 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.