MATHEMATICA BOHEMICA, Vol. 133, No. 1, pp. 63-74 (2008)

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

Tuo-Yeong Lee

Tuo-Yeong Lee, Mathematics and Mathematics Education, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Republic of Singapore, e-mail:

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

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