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Let $f$ be a function defined over $D \subseteq \mathbb{R}$.  $f$ is a step function, if and only if, 
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$\forall x_1, x_2 \in D$ with $x_1 < x_2, f(x_1) \neq f(x_2) \Rightarrow \exists z \in \mathbb{R}$, with $x_1 \leq z \leq x_2$, such that

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	\item $z \not\in D$, or
	\item $\lim_{x \to z^{-}} f(x) \neq  \lim_{x \to z^{+}} f(x)$
\end{itemize}

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