Real Analysis Exchange

The Radon-Nikodým Theorem for the Henstock integral in the Euclidean space

Ng Wee Leng and Lee Peng Yee

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We prove the Radon-Nikodým theorem for the Henstock integral and hence give a complete characterization of the primitive of a Henstock integrable function in Euclidean space.

Article information

Real Anal. Exchange, Volume 22, Number 2 (1996), 677-687.

First available in Project Euclid: 22 May 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Henstock integral \(ACG_{\Delta}\) Radon-Nikodým theorem (L)-condition basic condition


Yee, Lee Peng; Leng, Ng Wee. The Radon-Nikodým Theorem for the Henstock integral in the Euclidean space. Real Anal. Exchange 22 (1996), no. 2, 677--687.

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  • R. Henstock, Lectures on the Theory of Integration, World Scientific, 1988.
  • E. Hewitt and K. Stromberg, Real and Abstract Analysis, Springer-Verlag, New York, Heidelberg, Berlin, 1969.
  • P. Y. Lee, Lanzhou Lectures on Henstock Integration, World Scientific, 1989.
  • P. Y. Lee, Measurability and the Henstock Integral, Proc. Internat. Math. Conf. 94, Kaohsiung, World Scientific, 1995, 99–106.
  • P. Y. Lee and T. S. Chew, Integration of Highly Oscillatory Functions in the Plane, Proc. Asian Math. Conf. 1990, Hong Kong, World Scientific, 1992, 277–279.
  • S. Saks, Theory of the Integral, 2nd ed. revised, New York, 1937.