It is proved that $fg$ is Henstock–Kurzweil integrable on a compact interval ${\mathop{\prod}_{i=1}^{m}}[a_i, b_i]$ in ${\mathbb R}^m$ for each Henstock–Kurzweil integrable function $f$ if and only if there exists a finite signed Borel measure $\nu$ on ${\mathop{\prod}_{i=1}^{m}}[a_i, b_i)$ such that $g$ is equivalent to $\nu({\mathop{\prod}_{i=1}^{m}}[a_i, \,{\cdot}\,))$ on ${\mathop{\prod}_{i=1}^{m}}[a_i, b_i]$.