| Title:
|
On the strong McShane integral of functions with values in a Banach space (English) |
| Author:
|
Schwabik, Štefan |
| Author:
|
Guoju, Ye |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
4 |
| Year:
|
2001 |
| Pages:
|
819-828 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The classical Bochner integral is compared with the McShane concept of integration based on Riemann type integral sums. It turns out that the Bochner integrable functions form a proper subclass of the set of functions which are McShane integrable provided the Banach space to which the values of functions belong is infinite-dimensional. The Bochner integrable functions are characterized by using gauge techniques. The situation is different in the case of finite-dimensional valued vector functions. (English) |
| Keyword:
|
Bochner integral |
| Keyword:
|
strong McShane integral |
| MSC:
|
26A39 |
| MSC:
|
28-02 |
| MSC:
|
28B05 |
| MSC:
|
46G10 |
| idZBL:
|
Zbl 1002.28013 |
| idMR:
|
MR1864044 |
| . |
| Date available:
|
2009-09-24T10:47:27Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127688 |
| . |
| Reference:
|
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| Reference:
|
[2] R. Gordon: The McShane integral of Banach-valued functions.Illinois J. Math. 34 (1990), 557–567. Zbl 0685.28003, MR 1053562, 10.1215/ijm/1255988170 |
| Reference:
|
[3] R. Gordon: Riemann integration in Banach spaces.Rocky Mountain J. Math. 21 (1991), 923–949. Zbl 0764.28008, MR 1138145, 10.1216/rmjm/1181072923 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[6] S. Lang: Real and Functional Analysis.Springer-Verlag, New York, 1993. Zbl 0831.46001, MR 1216137 |
| Reference:
|
[7] Š. Schwabik: Abstract Bochner and McShane integrals.Ann. Math. Sil. 10 (1996), 21–56. Zbl 0868.28005, MR 1399609 |
| Reference:
|
[8] V. A. Skvortsov and A. P. Solodov: A variational integral for Banach-valued functions.Real Anal. Exchange 24 (1998/99), 799–806. MR 1704751 |
| Reference:
|
[9] P.-Y. Lee: Lanzhou Lectures on Henstock Integration.World Scientific, Singapore, 1989. Zbl 0699.26004, MR 1050957 |
| . |
