非可加集函数的Hahn分解

经典测度论中所涉及到的集函数是满足可加性要求的,Hahn分解理论是很重要的定理.在去掉可加性的条件下,将经典测度论中的某些概念加以推广,得到相应的结果.同时,也为经典可加测度的Hahn分解定理提供了更加清晰的证明方法.

广义 Fuzzy 测度的穷竭性、序连续性和 Jordan 分解

证明了广义Ｆｕｚｚｙ测度的穷竭性和序连续性是等价的。并在零零可加条件下证明了广义Ｆｕｚｚｙ测度Ｊｏｒｄａｎ分解的存在性，又在零可加条件下证明了Ｊｏｒｄａｎ分解的唯一性。

Pseudometric Generating Property of Fuzzy Measures Convergence in Fuzzy Measure

The relations among three kinds of structural characteristics of fuzzy measure: (1) pseudometric generating property; (2) pseudometric generating property of type p; (3) null null additivity, and the convergence for sequence of measurable function on semi continuous fuzzy measure space are discussed. A set of equivalent conditions for each of these structural characteristics are presented, respectively. It is proved that null null additivity is equivalent to pseudometric generating property for a finite fuzzy measure on S compact space.