| Title:
|
A continous version of Orlicz-Pettis theorem via vector-valued Henstock-Kurzweil integrals (English) |
| Author:
|
Fong, C. K. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
531-536 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that a Pettis integrable function from a closed interval to a Banach space is Henstock-Kurzweil integrable. This result can be considered as a continuous version of the celebrated Orlicz-Pettis theorem concerning series in Banach spaces. (English) |
| Keyword:
|
Pettis integrability |
| Keyword:
|
HK-integrals |
| Keyword:
|
Saks-Henstock’s property |
| MSC:
|
26A39 |
| MSC:
|
28A75 |
| MSC:
|
28B05 |
| MSC:
|
28E50 |
| MSC:
|
46G10 |
| idZBL:
|
Zbl 1011.28006 |
| idMR:
|
MR1923258 |
| . |
| Date available:
|
2009-09-24T10:53:44Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127740 |
| . |
| Reference:
|
[1] R. G. Bartle: Return to the Riemann integral.Amer. Math. Monthly 103 (1996), 625–632. Zbl 0884.26007, MR 1413583, 10.2307/2974874 |
| Reference:
|
[2] M. M. Day: Normed Linear Spaces.Academic Press Inc., New York, 1962. Zbl 0100.10802, MR 0145316 |
| Reference:
|
[3] J. Diestel: Sequences and Series in Banach Spaces.Springer-Verlag, New York, 1984. MR 0737004 |
| Reference:
|
[4] J. Diestel and J. J. Uhl, Jr.: Vector Measures. Mathematical Surveys, No. 15.Amer. Math. Soc., Providence, 1997. MR 0453964 |
| Reference:
|
[5] R. Henstock: The General Theory of Integration.Clarendon Press, Oxford, 1991. Zbl 0745.26006, MR 1134656 |
| Reference:
|
[6] W. F. Pfeffer: The Riemann Approach to Integration. Cambridge Tracts in Mathematics, No. 109.Cambridge University Press, Cambridge, 1993. MR 1268404 |
| Reference:
|
[7] E. M. Stein: Singular Integrals and Differentiability Properties of Functions.Princeton University Press, Princeton, 1970. Zbl 0207.13501, MR 0290095 |
| Reference:
|
[8] Š. Schwabik: Abstract Bochner and McShane Integrals.Ann. Math. Sil. 1564(10) (1996), 21–56. Zbl 0868.28005, MR 1399609 |
| . |
