\begin{definition}[Definition:Sampling Function/2 Dimensional]
Let $\operatorname {III}: \R \to \R$ denote the '''sampling function'''.
The $2$-dimensional form of $\operatorname {III}$ is defined and denoted:
:$\forall x, y \in \R: \map {\operatorname { {}^2 III} } {x, y} := \map {\operatorname {III} } x \map {\operatorname {III} } y$
\end{definition}