Tuo-Yeong Lee, Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Republic of Singapore, e-mail: tuoyeong.lee@nie.edu.sg
Abstract: 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.
Keywords: Henstock-Kurzweil integral, bounded variation in the sense of Hardy-Krause, integration by parts
Classification (MSC2000): mb133_1_6
Full text of the article: