2018/09/16 by Kaliaj, Sokol Bush
#46B25 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 28B05 #Secondary 46G10
paper · doi:10.48550/arxiv.1809.05939
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.