Conditions for Egoroff's theorem in non-additive measure theory

Fuzzy Sets and Systems

Volumn 146, Issue 1, 2004, Pages 135-146

  Murofushi, Toshiaki ^a   Uchino, Kenta ^a   Asahina, Shin ^a  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Almost everywhere convergence; Almost uniform convergence; Non additive measures

Indexed keywords

BOUNDARY CONDITIONS; FUZZY SETS; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; MATHEMATICAL TECHNIQUES; PROGRAM INTERPRETERS; SET THEORY;

ALMOST EVERYWHERE CONVERGENCE; ALMOST UNIFORM CONVERGENCE; EGOROFF'S THEOREM; NON-ADDITIVE MEASURES;

THEOREM PROVING;

EID: 3042548322     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2003.09.006     Document Type: Conference Paper

References (15)

1. Denneberg D. Non-Additive Measure and Integral. 2nd Edition:1997;Kluwer, Dordrecht.
2. Dobrakov I. On submeasures I. Dissertationes Math. 112:1974;1-35.
3. Ghirardato P. On independence for non-additive measures, with a Fubini theorem. J. Econom. Theory. 73:1997;261-291.
4. Gilboa I., Schmeidler D. Additive representations of non-additive measures and the Choquet integral. Ann. Oper. Res. 52:1994;43-65.
5. Li J. Order continuous of monotone set function and convergence of measurable functions sequence. Appl. Math. Comput. 135:2003;211-218.
6. Li J. On Egoroff. 's theorems on fuzzy measure spaces Fuzzy Sets and Systems. 135:2003;367-375.
7. Murofushi T., Sugeno M. A theory of fuzzy measures. representations, the Choquet integral, and null sets J. Math. Anal. Appl. 159:1991;532-549.
8. Murofushi T., Sugeno M., Suzaki M. Autocontinuity, convergence in measure, and convergence in distribution. Fuzzy Sets and Systems. 92:1997;197-203.
9. Pap E. Null-Additive Set Functions. 1995;Kluwer, Dordrecht.
10. Puri M.L., Ralescu D. A possibility measure is not a fuzzy measure. Fuzzy Sets and Systems. 7:1982;311-313.
11. M. Sugeno, Theory of fuzzy integrals and its applications, Doctoral Thesis, Tokyo Institute of Technology, 1974.
12. Sun Q. Property (S) of fuzzy measure and Riesz's theorem. Fuzzy Sets and Systems. 62:1994;117-119.
13. K. Uchino, T. Murofushi, Relations between mathematical properties of fuzzy measures, Proc. 10th IFSA World Congr., Istanbul, Turkey, 2003, pp. 27-30.
14. Wagner E., Wilczynski W. Convergence almost everywhere of sequences of measurable functions. Colloq. Math. 45:1981;119-124.
15. Wang Z., Klir G.J. Fuzzy Measure Theory. 1992;Plenum, New York.