Real Analysis Exchange

Notes on absolutely convergent integration

Yôto Kubota

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Abstract

We show that there exists an absolutely convergent integral which properly includes the Lebesgue integral and that any such integral does not have positive property as a functional.

Article information

Source
Real Anal. Exchange, Volume 22, Number 2 (1996), 856-859.

Dates
First available in Project Euclid: 22 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1337713167

Mathematical Reviews number (MathSciNet)
MR1460998

Zentralblatt MATH identifier
0941.26007

Subjects
Primary: 26A42: Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX] 26A30: Singular functions, Cantor functions, functions with other special properties

Keywords
absolutely convergent integration Lebesgue integral

Citation

Kubota, Yôto. Notes on absolutely convergent integration. Real Anal. Exchange 22 (1996), no. 2, 856--859. https://projecteuclid.org/euclid.rae/1337713167


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References

  • Y. Kubota, Notes on integration, Math. Japon., 31 (1986), 617–621.
  • Y. Kubota, A note on the Lebesgue integral, Soochow J. Math., 13 (1987), 65–67.
  • K. Kartak, A generalization of the Carathéodory theory of the differential equations, Czech. Math. J., 17 (1967), 482–514 (especially 484–487, 510–511).