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Dunford–Henstock–Kurzweil and Dunford–McShane Integrals of Vector-Valued Functions Defined on m-Dimensional Bounded Sets

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Abstract

In this paper, we define the Dunford–Henstock–Kurzweil and the Dunford–McShane integrals of Banach space-valued functions defined on a bounded Lebesgue measurable subset of m-dimensional Euclidean space \({\mathbb {R}}^{m}\). We will show that the new integrals are “natural” extensions of the McShane and the Henstock–Kurzweil integrals from m-dimensional closed non-degenerate intervals to m-dimensional bounded Lebesgue measurable sets. As applications, we will present full descriptive characterizations of the McShane and Henstock–Kurzweil integrals in terms of our integrals. Moreover, a relationship between new integrals will be proved in terms of the Dunford integral.

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  1. Mathematics Department, Science Natural Faculty, University of Elbasan, Elbasan, Albania

    Sokol Bush Kaliaj

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Kaliaj, S.B. Dunford–Henstock–Kurzweil and Dunford–McShane Integrals of Vector-Valued Functions Defined on m-Dimensional Bounded Sets. Mediterr. J. Math. 17, 136 (2020). https://doi.org/10.1007/s00009-020-01591-7

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  • DOI: https://doi.org/10.1007/s00009-020-01591-7

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