Publication at Faculty of Mathematics and Physics |
2008
Abstract
The Henstock-Kurzweil and McShane product integrals generalize the notion of 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 is absolutely continuous. As a consequence we obtain the result that the notion of McShane product integral of a matrix function coincides with the Bochner product integral.