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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  2. Artstein Z., Set-valued measures, Trans. Amer. Math. Soc. 165 (1972), 103-125. (1972) Zbl0237.28008MR0293054
  3. Amir D., Lindenstrauss J., The structure of weakly compact sets in Banach spaces, Ann. Math. 88 (1968), 35-46. (1968) Zbl0164.14903MR0228983
  4. Castaing C., Valadier M., Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer-Verlag, 1977. Zbl0346.46038MR0467310
  5. Diestel J., Uhl J., Vector Measures, Amer. Math. Soc., no. 15, 1977. Zbl0521.46035MR0453964
  6. Hiai F., Umegaki H., Integrals, conditional expectations and martingales of multivalued functions, J. Multivariate Anal. 7 (1977), 149-182. (1977) Zbl0368.60006MR0507504
  7. Hiai F., Radon-Nikodym theorems for set-valued measures, J. Multivariate Anal. 8 (1978), 96-118. (1978) Zbl0384.28006MR0583862
  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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