Real Analysis Exchange

The dual of the Henstock-Kurzweil space

Genqian Liu

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Abstract

We prove that if \(T\) is a continuous linear functional on the space \({\mathcal D}\) of Henstock-Kurzweil integrable functions on \([a_1,b_1] \times \cdots \times [a_m,b_m]\), then there exists a function \(g\) of strong bounded variation on \([a_1,b_1] \times \cdots \times [a_m,b_m]\) such that \[ T(f) = (HK) {\int \ldots \int \atop \scriptstyle{[a_1,b_1] \times \cdots \times [a_m,b_m]}} f(x_1,\ldots,x_m) g(x_1,\ldots,x_m)\, dx_1 \ldots dx_m\, . \]

Article information

Source
Real Anal. Exchange, Volume 22, Number 1 (1996), 105-121.

Dates
First available in Project Euclid: 1 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1338515207

Mathematical Reviews number (MathSciNet)
MR1433600

Zentralblatt MATH identifier
0879.26046

Subjects
Primary: 26A39: Denjoy and Perron integrals, other special integrals 26A42: Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX] 26B30: Absolutely continuous functions, functions of bounded variation

Keywords
Linear functionals Henstock-Kurzweil integral strong bounded variation

Citation

Liu, Genqian. The dual of the Henstock-Kurzweil space. Real Anal. Exchange 22 (1996), no. 1, 105--121. https://projecteuclid.org/euclid.rae/1338515207


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References

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