![](https://static.youtibao.com/asksite/comm/h5/images/m_q_title.png)
(X,)是可测空间,μ是(X,)上的有限实测度,A∈.若,EA,有μ(E)≥0,则称A为正集.若,EA,有μ(E)≤0,则称A为负集.证明下
(X,)是可测空间,μ是(X,
)上的有限实测度,A∈
.若
,E
A,有μ(E)≥0,则称A为正集.若
,E
A,有μ(E)≤0,则称A为负集.证明下述的Hahn分解定理:
存在正集A+和负集A-使,A+∪A-=X,且对
,有
μ+(E)=μ(A+∩E),μ-(E)=-μ(A-∩E).
这里X的分解(A+,A-)称为μ的Hahn分解.
![](https://static.youtibao.com/asksite/comm/h5/images/solist_ts.png)