Folland's proof of the Hahn Decomposition. Minor error? Theorem 3.3 of Folland's Real Analysis (ed 2) is the Hahn decomposition theorem. In the proof he assumes that the signed measure $\nu$ he is considering does not take the value $-\infty$. Then he argues:

Let $m$ be the supremum of $\nu(E)$ as $E$ ranges over all positive
  sets; thus there is a sequence $\{P_j\}$ of positive sets such that
  $\nu(P_j) \to m$. Let $P = \cup_1^\infty P_j$. By Lemma 3.2 and
  Proposition 3.1, $P$ is positive and $\nu(P)=m$; in particular, $m < \infty.$

The justification for the claim that $m<\infty$ is not clear to me. Could it be the case that Folland wanted to assume that $\nu$ does not take on the value $\infty$ in which case I think that the rest of the proof would work. Or am I missing something?

Yes, you are right. Folland did give an errata for his book which shows that $-\infty$ is a typo in the proof and it should be $+\infty$ instead. 
