\begin{definition}[Definition:Complex Measure]
Let $\struct {X, \Sigma}$ be a measurable space.
Let $\mu : \Sigma \to \C$ be a complex function.
We say that $\mu$ is a '''complex measure''' on $\struct {X, \Sigma}$ {{iff}}: 
{{begin-axiom}}
{{axiom | n = 1
        | ml= \map \mu \O
        | mo= =
        | mr= 0
}}
{{axiom | n = 2
        | q = \forall \sequence {S_n}_{n \mathop \in \N} \subseteq \Sigma: \forall i, j \in \N: S_i \cap S_j = \O
        | ml= \map \mu {\bigcup_{n \mathop = 1}^\infty S_n}
        | mo= =
        | mr= \sum_{n \mathop = 1}^\infty \map \mu {S_n}
        | rc= that is, $\mu$ is a countably additive function
}}
{{end-axiom}}
\end{definition}