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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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  • J. Diestel and J. J. Uhl Jr., Vector measures, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis; Mathematical Surveys, No. 15. MR 0453964
  • Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. General theory; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1958 original; A Wiley-Interscience Publication. MR 1009162
  • C. Godet-Thobie, Some results about multimeasures and their selectors, Measure theory, Oberwolfach 1979 (Proc. Conf., Oberwolfach, 1979) Lecture Notes in Math., vol. 794, Springer, Berlin, 1980, pp. 112–116. MR 577965
  • Igor Kluvánek and Greg Knowles, Vector measures and control systems, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1976. North-Holland Mathematics Studies, Vol. 20; Notas de Matemática, No. 58. [Notes on Mathematics, No. 58]. MR 0499068
  • R. Pallu de la Barrière, Multimesures à valeurs convexes fermées, Intégration vectorielle et multivoque (Colloq., Univ. Caen, Caen, 1975), Exp. No. 4, Dép. Math., U. E. R. Sci., Univ. Caen, Caen, 1975, pp. 30 (French). MR 0405101
  • 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