Korean J. Math. Vol. 22 No. 2 (2014) pp.383-393
DOI: https://doi.org/10.11568/kjm.2014.22.2.383

Convergence theorems for the Choquet-Pettis integral

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Published: Jun 26, 2014
Keywords:
fuzzy measure, Choquet integral, Choquet-Pettis integral, regular fuzzy measure
Mathematics Subject Classification:
26A39, 28A25, 28B05, 28E10

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Chun-Kee Park
Kangwon National Universiy

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.


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Supporting Agencies

This study was supported by 2013 Research Grant from Kangwon National University(No. 120131798)

References

[1] G. Choquet, Theory of capacities, Ann. Inst. Fourier 5 (1953), 131–295. Google Scholar

[2] D. Dellacherie, Quelques commentaires sur les prolongements de capacit es, S eminaire de Probabilit es 1969/1970, Strasbourg, Lecture Notes in Mathematics, 191 Springer, Berlin, 1971, 77-81. Google Scholar

[3] D. Denneberg, Non Additive Measure and Integral, Kluwer Academic Publishers,1994. Google Scholar

[4] J. Diestel, J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., 1977 Google Scholar

[5] 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. Google Scholar

[6] T. Murofushi, M. Sugeno, A theory of fuzzy measure representations, the Choquet integral, and null sets, J. Math. Anal. Appl. 159 (1991), 532–549. Google Scholar

[7] T. Murofushi, M. Sugeno, M. Suzaki, Autocontinuity, convergence in measure, and convergence in distribution, Fuzzy Sets and Systems 92 (1997), 197-203. Google Scholar

[8] Y. Narukawa, T. Murofushi, M. Sugeno, Regular fuzzy measure and represen- tation of comonotonically additive functions, Fuzzy Sets and Systems 112 (2) (2000), 177-186. Google Scholar

[9] M. Sugeno, Theory of fuzzy integrals and its applications, Dr. Thesis, Tokyo Institute of Technology, 1974. Google Scholar

[10] Z. Wang, G. Klir, W. Wang, Monotone set functions defined by Choquet integral, Fuzzy Sets and Systems 81 (1996), 241–250. Google Scholar

[11] D. Zhang, C. Guo, D. Liu, Set-valued Choquet integrals revisited, Fuzzy Sets and Systems 147 (2004), 475–485. Google Scholar