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http://dx.doi.org/10.11568/kjm.2014.22.2.383

CONVERGENCE THEOREMS FOR THE CHOQUET-PETTIS INTEGRAL  

Park, Chun-Kee (Department of Mathematics Kangwon National University)
Publication Information
Korean Journal of Mathematics / v.22, no.2, 2014 , pp. 383-393 More about this Journal
Abstract
In this paper, we introduce the concept of Choquet-Pettis integral of Banach-valued functions using the Choquet integral of real-valued functions and investigate convergence theorems for the Choquet-Pettis integral.
Keywords
fuzzy measure; Choquet integral; Choquet-Pettis integral; regular fuzzy measure;
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1 Z. Wang, G. Klir, W. Wang, Monotone set functions defined by Choquet integral, Fuzzy Sets and Systems 81 (1996), 241-250.   DOI   ScienceOn
2 T. Murofushi, M. Sugeno, M. Suzaki, Autocontinuity, convergence in measure, and convergence in distribution, Fuzzy Sets and Systems 92 (1997), 197-203.   DOI   ScienceOn
3 M. Sugeno, Theory of fuzzy integrals and its applications, Dr. Thesis, Tokyo Institute of Technology, 1974.
4 D. Zhang, C. Guo, D. Liu, Set-valued Choquet integrals revisited, Fuzzy Sets and Systems 147 (2004), 475-485.   DOI   ScienceOn
5 J. Diestel, J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., 1977
6 G. Choquet, Theory of capacities, Ann. Inst. Fourier 5 (1953), 131-295.
7 D. Dellacherie, Quelques commentaires sur les prolongements de capacites, Seminaire de Probabilites 1969/1970, Strasbourg, Lecture Notes in Mathematics, 191 Springer, Berlin, 1971, 77-81.
8 D. Denneberg, Non Additive Measure and Integral, Kluwer Academic Publishers, 1994.
9 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 (1959), 201-227.
10 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
11 Y. Narukawa, T. Murofushi, M. Sugeno, Regular fuzzy measure and representation of comonotonically additive functions, Fuzzy Sets and Systems 112 (2) (2000), 177-186.   DOI   ScienceOn