# Hahn Decomposition Proof

1. Dec 2, 2014

### nateHI

In the proof of the Hahn Decomposition Thm located here, there is the following sentence at the top of page 4.

"However, we shall prove that there is a positive subset of E carrying a positive charge, thereby obtaining the

but, if $G$ is the positive subset of $E$ mentioned above then
$G \subset E\subset N$ which implies that $N$ is not a negative set. That seems to support the incorrect assumption, not contradict it. What am I missing?

2. Dec 2, 2014

### mathman

I haven't gone through the details, but I think it is trying to show that $G\subset{P}$ contradicting $G\subset{N}$.

3. Dec 2, 2014

### nateHI

Yup. You're correct. Thanks, I was having a hard time with that one.