\begin{definition}[Definition:Negative 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 '''negative part''' of $\mu$.
\end{definition}