非可加集函数的Hahn分解

Hahn Decompositions of Non-additive Set Function

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.

As we know ,classical （signed） measure is a set function which is additive. Hahn decomposition theorem is very important. Some concepts for classical （signed） measure are generalized without additivity, and the corresponding results are made. At the same time, this paper provides a clearer proof method for classical additive measure.