The purpose of this paper is to investigate the convergence of sequence of measurable functions on fuzzy measure spaces. Several classical results on the convergence of measurable functions, such as Egoroff's theorem, Lebesgue's theorem and Riesz's theorem, are extended to fuzzy measure spaces by us
Space of fuzzy measures and convergence
β Scribed by Yasuo Narukawa; Toshiaki Murofushi; Michio Sugeno
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 230 KB
- Volume
- 138
- Category
- Article
- ISSN
- 0165-0114
No coin nor oath required. For personal study only.
β¦ Synopsis
The convergences of the net (generalized sequence) of fuzzy measures are discussed. It is shown that three types of convergence are not equivalent in general case, however they are equivalent if the universal set is ΓΏnite.
π SIMILAR VOLUMES
In this paper, on the Sugeno's fuzzy measures space, we ΓΏrst put forward the concepts of the weak convergence and the metric of fuzzy measures. And then, an equivalent condition on the weak convergence of sequences of fuzzy measure are given. Finally, in the sense of this metric, we obtain that the
The concepts of "fundamental almost everywhere" and "fundamental pseudo-almost everywhere" on fuzzy measure space are introduced, the relations among convergence of sequences of measurable functions are further discussed, the corresponding results on classical measure space are generalized and some
In this paper we introduce the notions of fuzzy upper limit, fuzzy lower limit and the fuzzy continuous convergence on the set of fuzzy continuous functions. In examining these aforementioned notions in the present paper we find on the one hand many properties of them whilst on the other, the follow