On Henstock--Kurzweil and McShane integrals of Banach space-valued functions
The problem of Henstock--Kurzweil integration of Banach space valued functions is studied with the aim to derive an analogue of a known result for the Perron integral of real functions saying that every Perron integrable function is such that every portion of the integration domain contains an interval on which the function is Lebesgue integrable. It turns out that such results hold for the case when the Banach space does not contain an isomorphic copy of the space \(c_0\). The McShane integral replaces the Lebesgue integral for infinite-dimensional Banach spaces. Various variants of results of this type are given in the paper.
scientific article; zbMATH DE number 5149490
scientific article