Definition 20.2.1 (Vector Measure).label Let $(X, \cm)$ be a measurable space, $E$ be a normed vector space over $K \in \RC$, and $\mu: \cm \to E$, then $\mu$ is a vector measure if:

1. (M1)

   $\mu(\emptyset) = 0$.

2. (M2)

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