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Lusin's theorem on fuzzy measure spaces

✍ Scribed by Jun Li; Masami Yasuda

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 258 KB
Volume: 146
Category: Article
ISSN: 0165-0114
DOI: 10.1016/s0165-0114(03)00207-0

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✦ Synopsis

In this paper, we show that weakly null-additive fuzzy measures on metric spaces possess regularity. Lusin's theorem, which is well-known in classical measure theory, is generalized to fuzzy measure space by using the regularity and weakly null-additivity. A version of Egoro 's theorem for the fuzzy measure deÿned on metric spaces is given. An application of Lusin's theorem to approximation in the mean of measurable function on fuzzy measure spaces is presented.

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