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Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrability of strongly measurable functions. (English) Zbl 1112.26015

Summary: We study the integrability of Banach valued strongly measurable functions defined on \([0,1]\). In case of functions \(f\) given by \(\sum _{n=1}^{\infty } x_n\chi _{E_n}\), where \(x_n \) belong to a Banach space and the sets \(E_n\) are Lebesgue measurable and pairwise disjoint subsets of \([0,1]\). We give some conditions for the Kurzweil-Henstock and the Kurzweil-Henstock-Pettis integrability of such functions.

MSC:

26A42 Integrals of Riemann, Stieltjes and Lebesgue type
26A39 Denjoy and Perron integrals, other special integrals
26A45 Functions of bounded variation, generalizations

Keywords:

Pettis integral
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