摘要
本文引进了关于某经典测度m连续的模糊测度的概念,证明如下的扩张定理: 定理:设X是一个集合,F是X上的一个域,m是定义在σ(F)上的一个全有限的测度。那么任意一个定义在F上且关于m连续的模糊测度可以唯一地扩张到σ(F)上。
In this paper, we introduce a class F fuzzy measures which are continuous with respect to a classical measure, and prove the following extension theorem.Theorem. Suppose that X is a set, F is a field on X, and that m is a totally finite measure defined on o(F). Then any fuzzy measure which is defined on F and continuous with respect to m can be extended uniquely to 0(F).
出处
《河北大学学报（自然科学版）》
CAS
1984年第2期97-101,共5页
Journal of Hebei University(Natural Science Edition)
