Search results for "Pettis integral"
showing 3 items of 43 documents
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 Riemann sums method in the Theory of vector Integration
2010
A first return examination of vector valued integrals.
2009
We prove that for each Bochner integrable function f there exists a trajectory yielding the Bochner integral of f, and that on infinite dimensional Banach spaces there exist Pettis integrable functions f such that no trajectory yields the Pettis integral of f.