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A multidimensional integration by parts formula for the Henstock-Kurzweil integral. (English) Zbl 1199.26029

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

MSC:

26A39 Denjoy and Perron integrals, other special integrals
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