A multidimensional integration by parts formula for the Henstock-Kurzweil integral
Mathematica Bohemica, Tome 133 (2008) no. 1, pp. 63-74.

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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.
DOI : 10.21136/MB.2008.133945
Classification : 26A39
Mots-clés : Henstock-Kurzweil integral; bounded variation in the sense of Hardy-Krause; integration by parts 
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Lee, Tuo-Yeong. A multidimensional integration by parts formula for the Henstock-Kurzweil integral. Mathematica Bohemica, Tome 133 (2008) no. 1, pp. 63-74. doi : 10.21136/MB.2008.133945. https://geodesic-test.mathdoc.fr/articles/10.21136/MB.2008.133945/

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