\begin{definition}[Definition:Integrable Function/p-Integrable]
Let $\struct {X, \Sigma, \mu}$ be a measure space.
Let $f \in \MM_{\overline \R}, f: X \to \overline \R$ be a measurable function.
Let $p \ge 1$ be a real number.
Then $f$ is said to be '''$p$-integrable in respect to $\mu$''' {{iff}}:
:$\ds \int \size f^p \rd \mu < +\infty$
is $\mu$-integrable.
\end{definition}