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Simple properties of PUL-Stieltjes integral in Banach space. (English) Zbl 1390.26014

Summary: Using PUL integrals, V. Boonpogkrong in [Taiwanese J. Math. 15, No. 2, 559–571 (2011; Zbl 1234.26020)] defined and discussed the Kurzweil-Henstock integral on manifolds. In this paper, we introduce the PUL-Stieltjes integral of Banach-valued functions and give some simple properties of this integral. Moreover, a characterization of PUL-Stieltjes integral is also given by establishing the Cauchy criterion.

MSC:

26A42 Integrals of Riemann, Stieltjes and Lebesgue type
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