\begin{definition}[Definition:Heaviside Step Function/Two Variables]
Let $u: \R \to \R$ be the Heaviside step function.
Then the '''Heaviside step function of two variables''' is the real function $u : \R^2 \to \R$ defined as the product of two step functions of one variable:
:$\map u {x, y} := \map u x \map u y$
In other words:
:$\map u {x, y} := \begin{cases}
1 & : \paren {x > 0} \land \paren {y > 0} \\
0 & : \text {otherwise}
\end{cases}$
{{research|something about products of step functions; namely, that they are applied sequentially and not at once}}
{{NamedforDef|Oliver Heaviside|cat = Heaviside}}
\end{definition}