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On the extension of multimeasures and integration with respect to a multimeasure

Author: Dimitrios A. Kandilakis
Journal: Proc. Amer. Math. Soc. 116 (1992), 85-92
MSC: Primary 28B05; Secondary 28B20, 46G10
MathSciNet review: 1091184
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Abstract: We present a Caratheodory-Hahn-Kluvanek-type theorem for multimeasures whose values are weakly compact and convex subsets of a Banach space. Set functions obtained by integrating a bounded measurable function with respect to a multimeasure are also studied.

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  • [1] I. Deistel and J. J. Uhl, Vector measures, Math. Surveys, vol. 15, Amer. Math. Soc., Providence, RI, 1977. MR 0453964 (56:12216)
  • [2] N. Dunford and J. Schwartz, Linear operators, Part I, Wiley Interscience, New York, 1988. MR 1009162 (90g:47001a)
  • [3] C. Godet-Thobie, Some results about multimeasures and their selectors, Measure Theory at Oberwohlfach, 1979 (Kölzow, ed.), Lecture Notes in Math., vol. 794, Springer, Berlin and New York, 1979, pp. 112-116. MR 577965 (81g:28011)
  • [4] I. Kluvanek and G. Knowles, Vector measures and control systems, North-Holland, Amsterdam, 1975. MR 0499068 (58:17033)
  • [5] R. Pallu de Barriere, Multimeasures a valeurs convexes fermees, Colloque sur l'Intergration Vectoriel et Multivoque (A. Coste, ed.) expose no. 4, Caen, 1975. MR 0405101 (53:8897)
  • [6] N. S. Papagergiou, On the properties of multimeasures with values in a Banach space, Comment. Math. Univ. Carolin, (to appear).

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Keywords: Set valued function, measure, multimeasure, support function, selector, weak compactness, uniformly strongly additive
Article copyright: © Copyright 1992 American Mathematical Society

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