Set valued measures and integral representation

Xiao Ping Xue; Cheng Lixin; Goucheng Li; Xiao Bo Yao

Commentationes Mathematicae Universitatis Carolinae (1996)

  • Volume: 37, Issue: 2, page 269-284
  • ISSN: 0010-2628

Abstract

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The extension theorem of bounded, weakly compact, convex set valued and weakly countably additive measures is established through a discussion of convexity, compactness and existence of selection of the set valued measures; meanwhile, a characterization is obtained for continuous, weakly compact and convex set valued measures which can be represented by Pettis-Aumann-type integral.

How to cite

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Xue, Xiao Ping, et al. "Set valued measures and integral representation." Commentationes Mathematicae Universitatis Carolinae 37.2 (1996): 269-284. <http://eudml.org/doc/247916>.

@article{Xue1996,
abstract = {The extension theorem of bounded, weakly compact, convex set valued and weakly countably additive measures is established through a discussion of convexity, compactness and existence of selection of the set valued measures; meanwhile, a characterization is obtained for continuous, weakly compact and convex set valued measures which can be represented by Pettis-Aumann-type integral.},
author = {Xue, Xiao Ping, Lixin, Cheng, Li, Goucheng, Yao, Xiao Bo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {set valued functions; set valued measures; Pettis-Aumann integral; boundedly -additive set-valued measure; strongly additive; weakly countably additive; vector measures; Pettis-Aumann type integral},
language = {eng},
number = {2},
pages = {269-284},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Set valued measures and integral representation},
url = {http://eudml.org/doc/247916},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Xue, Xiao Ping
AU - Lixin, Cheng
AU - Li, Goucheng
AU - Yao, Xiao Bo
TI - Set valued measures and integral representation
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1996
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 37
IS - 2
SP - 269
EP - 284
AB - The extension theorem of bounded, weakly compact, convex set valued and weakly countably additive measures is established through a discussion of convexity, compactness and existence of selection of the set valued measures; meanwhile, a characterization is obtained for continuous, weakly compact and convex set valued measures which can be represented by Pettis-Aumann-type integral.
LA - eng
KW - set valued functions; set valued measures; Pettis-Aumann integral; boundedly -additive set-valued measure; strongly additive; weakly countably additive; vector measures; Pettis-Aumann type integral
UR - http://eudml.org/doc/247916
ER -

References

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  8. Ionescu-Tulcea A., Ionescu-Tulcea C., Topics in the Theory of Lifting, Springer-Verlag, Berlin, 1969. Zbl0179.46303
  9. Papageorgiou N., On the theory of Banach space valued multifunctions, J. Multivariate Anal. 17 (1985), 185-227. (1985) Zbl0579.28010MR0808276
  10. Papageorgiou N., Representation of set-valued operators, Trans. Amer. Math. Soc. 292 (1985), 557-572. (1985) Zbl0605.46037MR0808737
  11. Papageorgiou N., Contributions to the theory of set-valued functions and set-valued measures, Trans. Amer. Math. Soc. 304 (1987), 245-265. (1987) Zbl0634.28004MR0906815
  12. Uhl J., The range of vector-valued measure, Proc. Amer. Math. Soc 23 (1969), 158-163. (1969) MR0264029
  13. Wilansky A., Modern Methods in Topological Vector Spaces, McGraw-Hill Inc., 1978. Zbl0395.46001MR0518316

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