| Title:
|
Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrability of strongly measurable functions (English) |
| Author:
|
Bongiorno, B. |
| Author:
|
Di Piazza, Luisa |
| Author:
|
Musiał, K. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
131 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
211-223 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the integrability of Banach valued strongly measurable functions defined on $[0,1]$. In case of functions $f$ given by $\sum _{n=1}^{\infty } x_n\chi _{E_n}$, where $x_n $ belong to a Banach space and the sets $E_n$ are Lebesgue measurable and pairwise disjoint subsets of $[0,1]$, there are well known characterizations for the Bochner and for the Pettis integrability of $f$ (cf Musial (1991)). In this paper we give some conditions for the Kurzweil-Henstock and the Kurzweil-Henstock-Pettis integrability of such functions. (English) |
| Keyword:
|
Kurzweil-Henstock integral |
| Keyword:
|
Kurzweil-Henstock-Pettis integral |
| Keyword:
|
Pettis integral |
| MSC:
|
26A39 |
| MSC:
|
26A42 |
| MSC:
|
26A45 |
| MSC:
|
28B05 |
| idZBL:
|
Zbl 1112.26015 |
| idMR:
|
MR2242846 |
| DOI:
|
10.21136/MB.2006.134086 |
| . |
| Date available:
|
2009-09-24T22:25:49Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134086 |
| . |
| Reference:
|
[1] A. Alexiewicz: Linear functionals on Denjoy integrable functions.Coll. Math. 1 (1948), 289–293. Zbl 0037.32302, MR 0030120, 10.4064/cm-1-4-289-293 |
| Reference:
|
[2] B. Bongiorno: The Henstock-Kurzweil integral.Handbook of Measure Theory I, E. Pap ed., Elsevier Amsterdam, 2002, pp. 587–615. Zbl 1024.26004, MR 1954623 |
| Reference:
|
[3] J. Diestel, J. J. Uhl: Vector measures.Math. Surveys, vol. 15, AMS, Providence, R.I., 1977. MR 0453964 |
| Reference:
|
[4] D. H. J. Fremlin: The Henstock and McShane integrals of vector-valued functions.Illinois J. Math. 38 (1994), 471–479. Zbl 0797.28006, MR 1269699, 10.1215/ijm/1255986726 |
| Reference:
|
[5] J. L. Gamez, J. Mendoza: On Denjoy-Dunford and Denjoy-Pettis integrals.Studia Math. 130 (1998), 115–133. MR 1623348 |
| Reference:
|
[6] P. Y. Lee: Lanzhou Lectures on Henstock Integration.World Scientific, Singapore, 1989. Zbl 0699.26004, MR 1050957 |
| Reference:
|
[7] K. Musial: Topics in the theory of Pettis integration.Rend. Istit. Mat. Univ. Trieste 23 (1991), 177–262. Zbl 0798.46042, MR 1248654 |
| Reference:
|
[8] C. Swartz: Norm convergence and uniform integrability for the Kurzweil-Henstock integral.Real Anal. Exchange 24 (1998/99), 423–426. MR 1691761 |
| . |
