6533b826fe1ef96bd1284215
RESEARCH PRODUCT
Approximation by step functions of Banach space valued nonabsolute integrals.
Benedetto BongiornoLuisa Di PiazzaK. Musialsubject
Pettis integral Henstock integral Henstock-Kurzweil-Pettis integral Denjoy-Khintchine-Pettis integral.Settore MAT/05 - Analisi Matematicadescription
The approximation of Banach space valued nonabsolutely integrable functions by step functions is studied. It is proved that a Henstock integrable function can be approximated by a sequence of step functions in the Alexiewicz norm, while a Henstock-Kurzweil-Pettis and a Denjoy-Khintchine-Pettis integrable function can be only scalarly approximate in the Alexiewicz norm by a sequence of step functions. In case of Henstock-Kurzweil-Pettis and Denjoy-Khintchine-Pettis integrals the full approximation can be done if and only if the range of the integral is norm relatively compact. It is also proved that if the target Banach space X does not contain any isomorphic copy of c_0, then the range of the integral of each X valued Denjoy-Khintchine-Pettis integrable function is norm relatively compact.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-01-01 |