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1996/1997 The dual of the Henstock-Kurzweil space
Genqian Liu
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Real Anal. Exchange 22(1): 105-121 (1996/1997).


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 \[ T(f) = (HK) {\int \ldots \int \atop \scriptstyle{[a_1,b_1] \times \cdots \times [a_m,b_m]}} f(x_1,\ldots,x_m) g(x_1,\ldots,x_m)\, dx_1 \ldots dx_m\, . \]


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Genqian Liu. "The dual of the Henstock-Kurzweil space." Real Anal. Exchange 22 (1) 105 - 121, 1996/1997.


Published: 1996/1997
First available in Project Euclid: 1 June 2012

zbMATH: 0879.26046
MathSciNet: MR1433600

Primary: 26A39 , 26A42 , 26B30

Keywords: Henstock-Kurzweil integral , linear functionals , strong bounded variation

Rights: Copyright © 1996 Michigan State University Press

Vol.22 • No. 1 • 1996/1997
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