Keywords: weak compactness; measurable multifunctions; Radon-Nikodym property; multimeasures
@article{CMJ_2001_51_3_a4,
author = {B\'arcenas, Diomedes},
title = {Weak compactness criteria for set valued integrals and {Radon} {Nikodym} {Theorem} for vector valued multimeasures},
journal = {Czechoslovak Mathematical Journal},
pages = {493--504},
year = {2001},
volume = {51},
number = {3},
mrnumber = {1851543},
zbl = {1079.28501},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_2001_51_3_a4/}
}
TY - JOUR AU - Bárcenas, Diomedes TI - Weak compactness criteria for set valued integrals and Radon Nikodym Theorem for vector valued multimeasures JO - Czechoslovak Mathematical Journal PY - 2001 SP - 493 EP - 504 VL - 51 IS - 3 UR - http://geodesic.mathdoc.fr/item/CMJ_2001_51_3_a4/ LA - en ID - CMJ_2001_51_3_a4 ER -
Bárcenas, Diomedes. Weak compactness criteria for set valued integrals and Radon Nikodym Theorem for vector valued multimeasures. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 3, pp. 493-504. http://geodesic.mathdoc.fr/item/CMJ_2001_51_3_a4/
[1] Z. Arststein: Weak convergence of set valued functions and control. SIAM, J. Control Optim. 13 (1975), 865–878. | DOI | MR
[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
[3] D. Barcenas and W. Urbina: Measurable multifunctions in non separable Banach spaces. SIAM, J. Math. Anal. 28 (1997), 1212–1226. | DOI | MR
[4] C. Castaing: Weak compactness criteria in set valued integration. Laboratorie d’Analyse convex, prepublication 1995/03. | Zbl
[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
[6] C. Castaing and M. Valadier: Convex Analysis and Measurable Multifunctions. LNM 586, Springer Verlag, Berlin, 1977. | MR
[7] W. J. Davis, T. Fiegel, W. B. Johnson and A. Pełczyński: Factoring weakly compact operators. J. Funct. Anal. 17 (1974), 311–327. | DOI | MR
[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. | DOI | MR
[9] J. Diestel, J. J. Uhl: Vector measures. Amer. Math. Soc. Surveys vol. 15, Providence, R.I., 1977. | MR
[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. | MR | Zbl
[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. | DOI | MR
[12] F. Hiai: Radon-Nikodym theorems for set valued measures. J. Multivariate Anal. 8 (1978), 96–118. | DOI | MR | Zbl
[13] F. Hiai and H. Umegaki: Integrals, conditional expectations and martingales of multivalued functions. J. Multivariate Anal. 7 (1977), 149–182. | DOI | MR
[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.
[15] M. Muresan: On a boundary value problem for quasi-linear differential inclusions of evolution. Collect. Math. 45 (1994), 165–175. | MR | Zbl
[16] N. Papageorgiou: Contributions to the theory of set valued functions and set valued measures. Trans. Amer. Math. Soc. 304 (1987), 245–265. | DOI | MR | Zbl
[17] N. Papageorgiou: Boundary value problems for evolution inclusions. Comment. Math. Univ. Carolin. 29 (1988), 355–363. | MR | Zbl
[18] N. Papageorgiou: Decomponsable sets in the Lebesgue Bochner spaces. Comment. Math. Univ. St. Paul 37 (1988), 49–62. | MR
[19] N. Papageorgiou: Radon-Nikodym theorem for multimeasures and transition multimeasures. Proc. Amer. Math. Soc. 111 (1991), 465–474. | MR
[20] N. Papageorgiou: On the convergence properties of measurable multifuntions in a Banach space. Math. Japon. 37 (1992), 637–643. | MR
[21] N. Papageorgiou: On the conditional expectation and convergence properties of Radon sets. Trans. Amer. Math. Soc. 347 (1995), 2495–2515. | DOI | MR
[22] H. P. Rosenthal: A characterization of Banach spaces containing $l^1$. Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 2411–2413. | DOI | MR
[23] C. Stegall: The Radon-Nikodym property in conjugate Banach Spaces II. Trans. Amer. Math. Soc. 264 (1981), 507–519. | MR | Zbl
[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