\begin{definition}[Definition:Positive Part of Signed Measure]
Let $\struct {X, \Sigma}$ be a measurable space.
Let $\mu$ be a signed measure on $\struct {X, \Sigma}$. 
Let $\tuple {\mu^+, \mu^-}$ be the Jordan decomposition of $\mu$.
We say that $\mu^+$ is the '''positive part''' of $\mu$.
\end{definition}