\begin{definition}[Definition:Simple Function]
Let $\struct {X, \Sigma}$ be a measurable space.
A real-valued function $f: X \to \R$ is said to be a '''simple function''' {{iff}} it is a finite linear combination of characteristic functions:
:$\ds f = \sum_{k \mathop = 1}^n a_k \chi_{S_k}$
where $a_1, a_2, \ldots, a_n$ are real numbers and each of the sets $S_k$ is $\Sigma$-measurable.
\end{definition}