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arXiv · 1809.05939

Dunford-Henstock-Kurzweil and Dunford-Mcshane integrals of vector-valued functions defined on m-dimensional bounded sets

Sokol Bush Kaliaj
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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 Rm. 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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Sokol Bush Kaliaj. 2018-09-16. Dunford-Henstock-Kurzweil and Dunford-Mcshane integrals of vector-valued functions defined on m-dimensional bounded sets. https://arxiv.org/abs/1809.05939

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