Definition 16.1.2 (Complex Measure). Let $(X, \cm)$ be a measurable space and $\mu: \cm \to \complex$, then $\mu$ is a complex measure if

1. $\mu(\emptyset) = 0$.

2. For any $\seq{E_n}\subset \cm$ pairwise disjoint, $\mu\paren{\bigsqcup_{n \in \natp}E_n}= \sum_{n \in \natp}\mu(E_{n})$ where the sum converges absolutely.