\begin{definition}[Definition:Integrable Function/Measure Space]
Let $\struct {X, \Sigma, \mu}$ be a measure space.
Let $f \in \MM_{\overline \R}, f: X \to \overline \R$ be a measurable function.
Then $f$ is said to be '''$\mu$-integrable''' {{iff}}:
:$\ds \int f^+ \rd \mu < +\infty$
and
:$\ds \int f^- \rd \mu < +\infty$
where $f^+$, $f^-$ are the positive and negative parts of $f$, respectively.
The integral signs denote $\mu$-integration of positive measurable functions.
\end{definition}