Abstract
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].
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Supported by grant No. 201/04/0690 of the Grant Agency of the Czech Republic.
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Slavík, A., Schwabik, Š. Henstock-Kurzweil and McShane product integration; Descriptive definitions. Czech Math J 58, 241–269 (2008). https://doi.org/10.1007/s10587-008-0015-x
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DOI: https://doi.org/10.1007/s10587-008-0015-x