# zbMATH — the first resource for mathematics

On Egoroff’s theorems on fuzzy measure spaces. (English) Zbl 1014.28015
Summary: In this paper, we show that Egoroff’s theorem, which is well known in classical measure theory, remains valid for a fuzzy measure without any additional condition. Previous results obtained by Z. Wang and others are improved. Egoroff’s theorem on fuzzy measure spaces is formulated in full generality. Taylor’s theorem which concerns convergence almost everywhere in classical measure theory is also extended to fuzzy measure spaces.

##### MSC:
 2.8e+11 Fuzzy measure theory
##### Keywords:
non-additive measures; fuzzy measure; Egoroff’s theorem
Full Text:
##### References:
  Halmos, P.R., Measure theory, (1968), Van Nostrand New York  Li, J.; Yasuda, M.; Jiang, Q.; Suzuki, H.; Wang, Z.; Klir, G.J., Convergence of sequence of measurable functions on fuzzy measure space, Fuzzy sets and systems, 87, 317-323, (1997) · Zbl 0915.28014  Liu, Y., Convergence of measurable set-valued function sequence on fuzzy measure space, Fuzzy sets and systems, 112, 241-249, (2000) · Zbl 0946.28013  Liu, X.; Zhang, G., Lattice-valued fuzzy measure and lattice-valued fuzzy integral, Fuzzy sets and systems, 62, 319-332, (1994) · Zbl 0824.28015  Pap, E., Null-additive set functions, (1995), Kluwer Dordrecht · Zbl 0856.28001  Ralescu, D.; Adams, G., The fuzzy integral, J. math. anal. appl., 75, 562-570, (1980) · Zbl 0438.28007  M. Sugeno, Theory of fuzzy integral and its applications, Ph.D. Thesis, Tokyo Institute of Technology, 1974.  Sun, Q., Property (s) of fuzzy measure and Riesz’s theorem, Fuzzy sets and systems, 62, 117-119, (1994) · Zbl 0824.28014  Taylor, S.J., An alternative form of Egoroff’s theorem, Fund. math., 48, 169-174, (1960) · Zbl 0098.26502  Wang, Z., The autocontinuity of set function and the fuzzy integral, J. math. anal. appl., 99, 195-218, (1984) · Zbl 0581.28003  Wang, Z., Asymptotic structural characteristics of fuzzy measure and their applications, Fuzzy sets and systems, 16, 277-290, (1985) · Zbl 0593.28007  Wang, Z.; Klir, G.J., Fuzzy measure theory, (1992), Plenum Press New York · Zbl 0812.28010  Zhang, G., Convergence of a sequence of fuzzy number-valued fuzzy measurable functions on the fuzzy number-valued fuzzy measure space, Fuzzy sets and systems, 57, 75-84, (1993) · Zbl 0783.28014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.