| Title:
|
Set valued measures and integral representation (English) |
| Author:
|
Xue, Xiaoping |
| Author:
|
Lixin, Cheng |
| Author:
|
Li, Goucheng |
| Author:
|
Yao, Xiaobo |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
269-284 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The extension theorem of bounded, weakly compact, convex set valued and weakly countably additive measures is established through a discussion of convexity, compactness and existence of selection of the set valued measures; meanwhile, a characterization is obtained for continuous, weakly compact and convex set valued measures which can be represented by Pettis-Aumann-type integral. (English) |
| Keyword:
|
set valued functions |
| Keyword:
|
set valued measures |
| Keyword:
|
Pettis-Aumann integral |
| MSC:
|
28A45 |
| MSC:
|
28B20 |
| MSC:
|
46G10 |
| idZBL:
|
Zbl 0885.28008 |
| idMR:
|
MR1399002 |
| . |
| Date available:
|
2009-01-08T18:23:36Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118832 |
| . |
| Reference:
|
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| Reference:
|
[2] Artstein Z.: Set-valued measures.Trans. Amer. Math. Soc. 165 (1972), 103-125. Zbl 0237.28008, MR 0293054 |
| Reference:
|
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| Reference:
|
[4] Castaing C., Valadier M.: Convex Analysis and Measurable Multifunctions.Lecture Notes in Math. 580, Springer-Verlag, 1977. Zbl 0346.46038, MR 0467310 |
| Reference:
|
[5] Diestel J., Uhl J.: Vector Measures.Amer. Math. Soc., no. 15, 1977. Zbl 0521.46035, MR 0453964 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Ionescu-Tulcea A., Ionescu-Tulcea C.: Topics in the Theory of Lifting.Springer-Verlag, Berlin, 1969. Zbl 0179.46303 |
| Reference:
|
[9] Papageorgiou N.: On the theory of Banach space valued multifunctions.J. Multivariate Anal. 17 (1985), 185-227. Zbl 0579.28010, MR 0808276 |
| Reference:
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[10] Papageorgiou N.: Representation of set-valued operators.Trans. Amer. Math. Soc. 292 (1985), 557-572. Zbl 0605.46037, MR 0808737 |
| Reference:
|
[11] Papageorgiou N.: Contributions to the theory of set-valued functions and set-valued measures.Trans. Amer. Math. Soc. 304 (1987), 245-265. Zbl 0634.28004, MR 0906815 |
| Reference:
|
[12] Uhl J.: The range of vector-valued measure.Proc. Amer. Math. Soc 23 (1969), 158-163. MR 0264029 |
| Reference:
|
[13] Wilansky A.: Modern Methods in Topological Vector Spaces.McGraw-Hill Inc., 1978. Zbl 0395.46001, MR 0518316 |
| . |
