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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Contributions to the theory of set valued functions and set valued measures


Author: Nikolaos S. Papageorgiou
Journal: Trans. Amer. Math. Soc. 304 (1987), 245-265
MSC: Primary 28B20; Secondary 46G10, 49A50, 54C60, 90A14
MathSciNet review: 906815
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Abstract: Measurable multifunctions and multimeasures with values in a Banach space are studied. We start by proving a variation of the known Dunford theorem for weak compactness in $ {L^1}(X)$. With a similar technique we prove that the range of certain vector valued integrals that appear in applications is $ w$-compact and convex. Also we obtain Dunford-Pettis type theorems for sequences of integrably bounded multifunctions. Some pointwise $ w$-compactness theorems are also obtained for certain families of measurable multifunctions. Then we prove a representation theorem for additive, set valued operators defined on $ {L^1}(X)$. Finally, in the last section, a detailed study of transition multimeasures is conducted and several representation theorems are proved.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0906815-3
PII: S 0002-9947(1987)0906815-3
Article copyright: © Copyright 1987 American Mathematical Society