Search results for "Kurzweil-Henstock integral"
showing 3 items of 13 documents
A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting
2015
Abstract A Kurzweil-Henstock type integral with respect to an abstract derivation basis in a topological measure space, for Riesz space-valued functions, is studied. A Hake-type theorem is proved for this integral, by using technical properties of Riesz spaces.
A decomposition of Denjoy-Khintchine-Pettis and Henstock-Kurzweil-Pettis integrable multifunctions
2010
We proved in one of our earlier papers that in case of separable Banach space valued multifunctions each Henstock-Kurzweil-Pettis integrable multifunction can be represented as a sum of one of its Henstock-Kurzweil-Pettis integrable selector and a Pettis integrable multifunction. Now, we prove that the same result can be achieved in case of an arbitrary Banach space. Moreover we show that an analogous result holds true also for the Denjoy-Khintchine-Pettis integrable multifunctions. Applying the representation theorem we describe the multipliers of HKP and DKP integrable functions. Then we use this description to obtain an operator characterization of HKP and DKP integrability.
A version of Hake’s theorem for Kurzweil–Henstock integral in terms of variational measure
2019
Abstract We introduce the notion of variational measure with respect to a derivation basis in a topological measure space and consider a Kurzweil–Henstock-type integral related to this basis. We prove a version of Hake’s theorem in terms of a variational measure.