Henstock-Kurzweil and McShane product integration; descriptive definitions

Antonín Slavík; Štefan Schwabik

Displaying similar documents to “Henstock-Kurzweil and McShane product integration; descriptive definitions”

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

Tuo-Yeong Lee (2008)

Mathematica Bohemica

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

Multipliers for generalized Riemann integrals in the real line

Tuo-Yeong Lee (2006)

Mathematica Bohemica

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We use an elementary method to prove that each $B V$ function is a multiplier for the $C$ -integral.

Substitution formulas for the Kurzweil and Henstock vector integrals

Márcia Federson (2002)

Mathematica Bohemica

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Results on integration by parts and integration by substitution for the variational integral of Henstock are well-known. When real-valued functions are considered, such results also hold for the Generalized Riemann Integral defined by Kurzweil since, in this case, the integrals of Kurzweil and Henstock coincide. However, in a Banach-space valued context, the Kurzweil integral properly contains that of Henstock. In the present paper, we consider abstract vector integrals of Kurzweil and...