【作者】 吴炯圻；

【Author】 Wu Jiong-qi (Department of Mathematics, Zhangzhou Teachel’s College, Zhang zhou, 363000, China)

【机构】 漳州师范学院数学系；

【摘要】 本文在广义模糊测度空间中引入仿正则的概念,探讨了它与正则的基本关系;利用Choquet型定理来研究广义模糊测度并证明了,度量空间X的Borel代数B(X)上的每一个有限的广义模糊测度都是仿正则的,即对任意A∈B(X),对任意ε>0,均存在开集G=G_ε和闭集F=F_ε只使得μ(G)<μ(F)+ε,这结论可看成关于通常测度的正则性定理的推广。更多还原

【Abstract】 The notion named para-regularity is introduced for the generalized fuzzy measures and the relation between para-regularity and the well-known regularity is discussed. The extended Choquet’ s Theorems are used to investigate generalized fuzzy measures and prove that every generalized fuzzy measure μ: B(X) →(-∞ ,∞ ) is para-regular where B(X) is the Borel algebra in a metric space X , i.e. for any set A∈B(X) and anyε> 0, there exist a closed subset B and an open subset G such thatB (?) A (?) G andμ(C) < μ(B) +ε. Our result can be considered as a generalization of the regularity theorem for the ordinary measure.更多还原