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http://dx.doi.org/10.11568/kjm.2012.20.4.381

SET-VALUED CHOQUET-PETTIS INTEGRALS  

Park, Chun-Kee (Department of Mathematics Kangwon National University)
Publication Information
Korean Journal of Mathematics / v.20, no.4, 2012 , pp. 381-393 More about this Journal
Abstract
In this paper, we introduce the Choquet-Pettis integral of set-valued mappings and investigate some properties and convergence theorems for the set-valued Choquet-Pettis integrals.
Keywords
set-valued mapping; Choquet integral; Choquet-Pettis integral;
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1 R.J. Aumann, Integrals of set-valued functions, J. Math. Anal. Appl. 12 (1965), 1-12.   DOI
2 G. Choquet, Lectures on Analysis, Vol. I, W.A. Benjamin, Inc. 1969.
3 G. Choquet, Theory of capacities, Ann. Inst. Fourier, Grenoble 5 (1955), 131- 295.
4 D. Dellacherie, Quelques commentaires sur les prolongements de capacites, Seminaire de Probabilites 1969/1970, Strasbourg, Lecture Notes in Mathematics , vol. 191 Springer, Berlin, 77-81, 1971.
5 D. Denneberg, Non Additive Measure and Integral, Kluwer Academic Publishers, 1994.
6 L. Di Piazza and K. Musial, A decomposition theorem for compact-valued Hen- stock integral, Monatsh. Math. 148 (2006), 119-126.   DOI
7 L. Di Piazza and K. Musial, Set-valued Kurzweil-Henstock-Pettis integral, Set-Valued Anal. 13 (2005), 167-179.   DOI   ScienceOn
8 J. Diestel, J.J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc. 1977.
9 K. El Amri and C. Hess, On the Pettis integral of closed valued multifunctions, Set-Valued Anal. 8 (2000), 329-360.   DOI
10 L.C. Jang, B.M. Kil, Y.K. Kim, J.S. Kwon, Some properties of Choquet integrals of set-valued functions, Fuzzy Sets and Systems, 91 (1997), 95-98.   DOI   ScienceOn
11 L.C. Jang, J.S. Kwon, On the representation of Choquet integrals of set-valued functions, and null sets, Fuzzy Sets and Systems, 112 (2000), 233-239.   DOI   ScienceOn
12 T. Murofushi, M. Sugeno, An interpretation of fuzzy measure and the Choquet integral as an integral with respect to a fuzzy measure, Fuzzy Sets and Systems 29 (1989), 201-227.   DOI   ScienceOn
13 T. Murofushi, M. Sugeno, A theory of fuzzy measure representations, the Choquet integral, and null sets, J. Math. Anal. Appl. 159 (1991), 532-549.   DOI
14 T. Murofushi, M. Sugeno, M. Suzaki, Autocontinuity, convergence in measure, and convergence in distribution, Fuzzy Sets and Systems 92 (1997), 197-203.   DOI   ScienceOn
15 W. Zhang, Z. Wang and Y. Gao, Set-Valued Stochastic Process, Academic Press, Beijing, 1996.
16 C.K. Park, On Choquet-Pettis integral, submitted.
17 M. Sugeno, Theory of fuzzy integrals and its applications, Dr. Thesis, Tokyo Institute of Technology, 1974.
18 D. Zhang, C. Guo, D. Liu, Set-valued Choquet integrals revisited, Fuzzy Sets and Systems 147 (2004), 475-485.   DOI   ScienceOn