Henstock-Kurzweil and McShane product integration; Descriptive definitions. (English) Zbl 1174.28013
Summary: 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 integrable on \([a,b]\).
MSC:
28B05 | Vector-valued set functions, measures and integrals |
References:
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