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Bounded linear functionals on the space of Henstock-Kurzweil integrable functions. (English) Zbl 1224.26026
Summary: Applying a simple integration by parts formula for the Henstock-Kurzweil integral, we obtain a simple proof of the Riesz representation theorem for the space of Henstock-Kurzweil integrable functions. Consequently, we give sufficient conditions for the existence and equality of two iterated Henstock-Kurzweil integrals.

MSC:
26A39 Denjoy and Perron integrals, other special integrals
46E99 Linear function spaces and their duals
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References:
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