A multidimensional integration by parts formula for the Henstock-Kurzweil integral

summary:It is shown that if $g$ is of bounded variation in the sense of Hardy-Krause on ${\mathop {\prod }\limits _{i=1}^{m}} [a_i, b_i]$, then $g \chi _{ _{{\mathop {\prod }\limits _{i=1}^{m}} (a_i, b_i)}}$ is of bounded variation there. As a result, we obtain a simple proof of Kurzweil’s multidimensional integration by parts formula