Title:
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Weak compactness criteria for set valued integrals and Radon Nikodym Theorem for vector valued multimeasures (English) |
Author:
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Bárcenas, Diomedes |
Language:
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English |
Journal:
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Czechoslovak Mathematical Journal |
ISSN:
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0011-4642 (print) |
ISSN:
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1572-9141 (online) |
Volume:
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51 |
Issue:
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3 |
Year:
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2001 |
Pages:
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493-504 |
Summary lang:
|
English |
. |
Category:
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math |
. |
Summary:
|
Some criteria for weak compactness of set valued integrals are given. Also we show some applications to the study of multimeasures on Banach spaces with the Radon-Nikodym property. (English) |
Keyword:
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weak compactness |
Keyword:
|
measurable multifunctions |
Keyword:
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Radon-Nikodym property |
Keyword:
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multimeasures |
MSC:
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28B05 |
MSC:
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28B20 |
MSC:
|
46G10 |
MSC:
|
47D06 |
MSC:
|
49J53 |
idZBL:
|
Zbl 1079.28501 |
idMR:
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MR1851543 |
. |
Date available:
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2009-09-24T10:44:38Z |
Last updated:
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2020-07-03 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/127665 |
. |
Reference:
|
[1] Z. Arststein: Weak convergence of set valued functions and control.SIAM, J. Control Optim. 13 (1975), 865–878. MR 0377661, 10.1137/0313052 |
Reference:
|
[2] I.Assani and A. Klei: Parties décomposables compactes de $L_E^1$.C. R. Acad. Sci. Paris, Ser. I 294 (1982), 533–536. MR 0679937 |
Reference:
|
[3] D. Barcenas and W. Urbina: Measurable multifunctions in non separable Banach spaces.SIAM, J. Math. Anal. 28 (1997), 1212–1226. MR 1466678, 10.1137/S0036141095296005 |
Reference:
|
[4] C. Castaing: Weak compactness criteria in set valued integration.Laboratorie d’Analyse convex, prepublication 1995/03. Zbl 0918.28014 |
Reference:
|
[5] C. Castaing and P. Clauzure: Compacite faible dans lespace des multifuntions integrablements bornees et minimizations.Ann. Mat. Pura Appl. (IV) 140 (1985), 345–364. MR 0807644 |
Reference:
|
[6] C. Castaing and M. Valadier: Convex Analysis and Measurable Multifunctions.LNM 586, Springer Verlag, Berlin, 1977. MR 0467310 |
Reference:
|
[7] W. J. Davis, T. Fiegel, W. B. Johnson and A. Pełczyński: Factoring weakly compact operators.J. Funct. Anal. 17 (1974), 311–327. MR 0355536, 10.1016/0022-1236(74)90044-5 |
Reference:
|
[8] J. Diestel and W. Ruess and W. Schachermayer: On weak copactness in $L^1(\mu ,X)$.Proc. Amer. Math. Soc. 118 (1993), 443–453. MR 1132408, 10.1090/S0002-9939-1993-1132408-X |
Reference:
|
[9] J. Diestel, J. J. Uhl: Vector measures.Amer. Math. Soc. Surveys vol. 15, Providence, R.I., 1977. MR 0453964 |
Reference:
|
[10] C. Godet Thobie: Some results about multimeasures and their selectors.Measure Theory, D. Kölzow (ed.), LNM 794, Springer-Verlag, Berlin, 1980, pp. 112–116. Zbl 0432.28009, MR 0577965 |
Reference:
|
[11] N. Ghoussoub and P. Saab: Weak compactness in spaces of Bochner integrable functions and the Radon-Nikodym property.Pacific J. Math. 110 (1984), 65–70. MR 0722738, 10.2140/pjm.1984.110.65 |
Reference:
|
[12] F. Hiai: Radon-Nikodym theorems for set valued measures.J. Multivariate Anal. 8 (1978), 96–118. Zbl 0384.28006, MR 0583862, 10.1016/0047-259X(78)90022-2 |
Reference:
|
[13] F. Hiai and H. Umegaki: Integrals, conditional expectations and martingales of multivalued functions.J. Multivariate Anal. 7 (1977), 149–182. MR 0507504, 10.1016/0047-259X(77)90037-9 |
Reference:
|
[14] H. A. Klein: A compactness criteria in $L^1(E)$ and Radon-Nikodym theorems for multimeasures.Bull. Soc. Math. 2ê serie 112 (1988), 305–324. |
Reference:
|
[15] M. Muresan: On a boundary value problem for quasi-linear differential inclusions of evolution.Collect. Math. 45 (1994), 165–175. Zbl 0824.34017, MR 1316934 |
Reference:
|
[16] N. Papageorgiou: 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, 10.1090/S0002-9947-1987-0906815-3 |
Reference:
|
[17] N. Papageorgiou: Boundary value problems for evolution inclusions.Comment. Math. Univ. Carolin. 29 (1988), 355–363. Zbl 0696.35074, MR 0957404 |
Reference:
|
[18] N. Papageorgiou: Decomponsable sets in the Lebesgue Bochner spaces.Comment. Math. Univ. St. Paul 37 (1988), 49–62. MR 0942305 |
Reference:
|
[19] N. Papageorgiou: Radon-Nikodym theorem for multimeasures and transition multimeasures.Proc. Amer. Math. Soc. 111 (1991), 465–474. MR 1036989 |
Reference:
|
[20] N. Papageorgiou: On the convergence properties of measurable multifuntions in a Banach space.Math. Japon. 37 (1992), 637–643. MR 1176035 |
Reference:
|
[21] N. Papageorgiou: On the conditional expectation and convergence properties of Radon sets.Trans. Amer. Math. Soc. 347 (1995), 2495–2515. MR 1290728, 10.1090/S0002-9947-1995-1290728-9 |
Reference:
|
[22] H. P. Rosenthal: A characterization of Banach spaces containing $l^1$.Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411–2413. MR 0358307, 10.1073/pnas.71.6.2411 |
Reference:
|
[23] C. Stegall: The Radon-Nikodym property in conjugate Banach Spaces II.Trans. Amer. Math. Soc. 264 (1981), 507–519. Zbl 0475.46016, MR 0603779 |
Reference:
|
[24] X. Xiaoping, C. Lixing, L. Goucheng and Y. Xiaobo: Set valued mesures and integral representations.Comment. Math. Univ. Carolin. 37 (1996), 269–284. MR 1399002 |
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