| Title:
|
The multiplier for the weak McShane integral (English) |
| Author:
|
Sayyad, Redouane |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
144 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
13-24 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The multiplier for the weak McShane integral which has been introduced by M. Saadoune and R. Sayyad (2014) is characterized. (English) |
| Keyword:
|
McShane integral |
| Keyword:
|
weak McShane integral |
| Keyword:
|
multiplier |
| MSC:
|
26A39 |
| MSC:
|
28B05 |
| MSC:
|
46G10 |
| idZBL:
|
Zbl 07088833 |
| idMR:
|
MR3934195 |
| DOI:
|
10.21136/MB.2018.0044-17 |
| . |
| Date available:
|
2019-03-21T12:29:53Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147636 |
| . |
| Reference:
|
[1] Piazza, L. Di, Marraffa, V.: An equivalent definition of the vector-valued McShane integral by means of partitions of unity.Stud. Math. 151 (2002), 175-185. Zbl 1005.28009, MR 1917952, 10.4064/sm151-2-5 |
| Reference:
|
[2] Dunford, N., Pettis, B. J.: Linear operations on summable functions.Trans. Am. Math. Soc. 47 (1940), 323-392. Zbl 0023.32902, MR 0002020, 10.2307/1989960 |
| Reference:
|
[3] Fremlin, D. H.: The generalized McShane integral.Ill. J. Math. 39 (1995), 39-67. Zbl 0810.28006, MR 1299648, 10.1215/ijm/1255986628 |
| Reference:
|
[4] Fremlin, D. H.: Measure Theory. Vol. 2. Broad Foundations.Torres Fremlin, Colchester (2003). Zbl 1165.28001, MR 2462280 |
| Reference:
|
[5] Fremlin, D. H.: Measure Theory. Vol. 4. Topological Measure Spaces. Part I, II.Torres Fremlin, Colchester (2006). Zbl 1166.28001, MR 2462372 |
| Reference:
|
[6] Geitz, R. F.: Pettis integration.Proc. Am. Math. Soc. 82 (1981), 81-86. Zbl 0506.28007, MR 0603606, 10.2307/2044321 |
| Reference:
|
[7] Hewitt, E., Stromberg, K.: Real and Abstract Analysis. A Modern Treatment of the Theory of Functions of a Real Variable.Graduate Texts in Mathematics 25. Springer, New York (1965). Zbl 0137.03202, MR 0188387, 10.1007/978-3-642-88047-6 |
| Reference:
|
[8] Musiał, K.: Vitali and Lebesgue convergence theorems for Pettis integral in locally convex spaces.Atti Semin. Mat. Fis. Univ. Modena 35 (1987), 159-165. Zbl 0636.28005, MR 0922998 |
| Reference:
|
[9] 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:
|
[10] Sayyad, R.: The McShane integral in the limit.Real Anal. Exch. 42 (2017), 283-310. MR 3721803, 10.14321/realanalexch.42.2.0283 |
| . |
