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Substitution formulas for the Kurzweil and Henstock vector integrals. (English) Zbl 1002.28012
Summary: Results on integration by parts and integration by substitution for the variational integral of Henstock are well-known. When real-valued functions are considered, such results also hold for the generalized Riemann integral defined by Kurzweil since, in this case, the integrals of Kurzweil and Henstock coincide. However, in a Banach space-valued context, the Kurzweil integral properly contains that of Henstock. In the present paper, we consider abstract vector integrals of Kurzweil and prove substitution formulas by functional analytic methods. In general, substitution formulas need not hold for Kurzweil vector integrals even if they are defined.

MSC:
28B05 Vector-valued set functions, measures and integrals
26A39 Denjoy and Perron integrals, other special integrals
46G10 Vector-valued measures and integration
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