| Title:
|
A remark on weak McShane integral (English) |
| Author:
|
Yoshitomi, Kazushi |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
69 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
45-53 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We characterize the weak McShane integrability of a vector-valued function on a finite Radon measure space by means of only finite McShane partitions. We also obtain a similar characterization for the Fremlin generalized McShane integral. (English) |
| Keyword:
|
weak McShane integral |
| Keyword:
|
finite McShane partition |
| Keyword:
|
Radon measure space |
| MSC:
|
28B05 |
| idZBL:
|
Zbl 07088768 |
| idMR:
|
MR3923573 |
| DOI:
|
10.21136/CMJ.2018.0153-17 |
| . |
| Date available:
|
2019-03-08T14:55:12Z |
| Last updated:
|
2021-04-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147616 |
| . |
| Reference:
|
[1] Bauer, H.: Measure and Integration Theory. De Gruyter Studies in Mathematics 26.Walter de Gruyter, Berlin (2001). Zbl 0985.28001, MR 1897176 |
| Reference:
|
[2] Faure, C.-A., Mawhin, J.: Integration over unbounded multidimensional intervals.J. Math. Anal. Appl. 205 (1997), 65-77. Zbl 0879.26047, MR 1426980, 10.1006/jmaa.1996.5172 |
| Reference:
|
[3] Fremlin, D. H.: Topological Riesz Spaces and Measure Theory.Cambridge University Press, London (1974). Zbl 0273.46035, MR 0454575 |
| Reference:
|
[4] Fremlin, D. H.: The generalized McShane integral.Ill. J. Math. 39 (1995), 39-67. Zbl 0810.28006, MR 1299648, 10.1215/ijm/1255986628 |
| Reference:
|
[5] Kelley, J. L., Srinivasan, T. P.: Measure and Integral Vol. 1. Graduate Texts in Mathematics 116.Springer, New York (1988). Zbl 0635.28001, MR 0918770, 10.1007/978-1-4612-4570-4 |
| Reference:
|
[6] Saadoune, M., Sayyad, R.: The weak McShane integral.Czech. Math. J. 64 (2014), 387-418. Zbl 1340.28016, MR 3277743, 10.1007/s10587-014-0108-7 |
| Reference:
|
[7] Schwabik, Š., Ye, G.: Topics in Banach Space Integration. Series in Real Analysis Vol. 10.World Scientific, Singapore (2005). Zbl 1088.28008, MR 2167754, 10.1142/9789812703286 |
| Reference:
|
[8] Talagrand, M.: Pettis integral and measure theory.Mem. Am. Math. Soc. 307 (1984),\99999MR99999 0756174 . Zbl 0582.46049, MR 0756174, 10.1090/memo/0307 |
| . |
