Geodesic
Henstock-Kurzweil and McShane product integration; descriptive definitions
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 1, pp. 241-269

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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 integrable on $[a,b]$.
Classification : 26A39, 28B05, 46G10
Keywords: Henstock-Kurzweil product integral; McShane product integral; Bochner product integral 
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     title = {Henstock-Kurzweil and {McShane} product integration; descriptive definitions},
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Slavík, Antonín; Schwabik, Štefan. Henstock-Kurzweil and McShane product integration; descriptive definitions. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 1, pp. 241-269. http://geodesic.mathdoc.fr/item/CMJ_2008__58_1_a14/