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 \[ T(f) = (HK) {\int \ldots \int \atop \scriptstyle{[a_1,b_1] \times \cdots \times [a_m,b_m]}} f(x_1,\ldots,x_m) g(x_1,\ldots,x_m)\, dx_1 \ldots dx_m\, . \]
Citation
Genqian Liu. "The dual of the Henstock-Kurzweil space." Real Anal. Exchange 22 (1) 105 - 121, 1996/1997.
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