Displaying similar documents to “Multipliers for generalized Riemann integrals in the real line”

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 ∏ i = 1 m [ a i , b i ] , then g χ ∏ 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.

Henstock-Kurzweil and McShane product integration; descriptive definitions

Antonín Slavík, Štefan Schwabik (2008)

Czechoslovak Mathematical Journal

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The Henstock-Kurzweil and McShane product integrals generalize the notion of the Riemann product integral. We study properties of the corresponding indefinite integrals (i.e. product integrals considered as functions of the upper bound of integration). It is shown that the indefinite McShane product integral of a matrix-valued function A is absolutely continuous. As a consequence we obtain that the McShane product integral of A over [ a , b ] exists and is invertible if and only if A is Bochner...