an:06513416
Zbl 1340.28021
Pova??an, Jaroslav; Rie??an, Beloslav
Fuzzy sets and small systems
EN
Brandts, J. (ed.) et al., Proceedings of the international conference `Applications of mathematics', Prague, Czech Republic, May 15--17, 2013. In honor of the 70th birthday of Karel Segeth. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-61-5). 185-187 (2013).
2013
a
28E10 28A20
Egorov theorem; fuzzy set; measure theory; monotone function
Summary: Independently with \textit{L. A. Zadeh} [Inf. Control 8, 338--353 (1965; Zbl 0139.24606)] a corresponding fuzzy approach has been developed in [\textit{T. Neubrunn}, Mat. ??as., Slovensk. Akad. Vied 19, 202--215 (1969; Zbl 0186.09801); \textit{B. Rie??an}, Mat.-Fyz. ??as., Slovensk. Akad. Vied 16, 268--273 (1966; Zbl 0174.34402); Mat. ??as., Slovensk. Akad. Vied 19, 138--144 (1969; Zbl 0193.00903)] with applications in measure theory. As one of the results, the Egorov theorem has been proved in an abstract form. In [\textit{J. Li}, ``Convergence theorems in monotone measure theory'', in: R. Mesiar (ed.) et al., Non-classical measures and integrals, 34th Linz seminar on fuzzy sets theory. 88--91 (2013)] a necessary and sufficient condition for holding the Egoroff theorem was presented in the case of a space with a monotone measure. By the help of [\textit{J. Li} and \textit{M. Yasuda}, Fuzzy Sets Syst. 153, No. 1, 71--78 (2005; Zbl 1077.28015)] and [\textit{B. Rie??an} and \textit{T. Neubrunn}, Integral, measure, and ordering. Dordrecht: Kluwer Academic Publishers (1997; Zbl 0916.28001)] we prove a variant of the Egorov theorem stated in [Zbl 0174.34402].
For the entire collection see [Zbl 1277.00032].
Zbl 0139.24606; Zbl 0186.09801; Zbl 0174.34402; Zbl 0193.00903; Zbl 1077.28015; Zbl 0916.28001