\begin{definition}[Definition:Integrable Function/Locally Integrable Function]
Let $f : \R^d \to \C$ be a function.
Let $K \subseteq \R^d$ be a compact subset.
Suppose:
:$\ds \forall K \subseteq \R^d : \int_K \size {\map f {\mathbf x} } \rd {\mathbf x} < \infty$
where $\mathbf x \in \R^d$ and $\rd {\mathbf x}$ and $\rd {\mathbf x} = \rd x_1 \rd x_2 \ldots \rd x_d$ is the volume element in $\R^d$.
Then $f$ is called the '''locally integrable function'''.
\end{definition}