Definition:Simple Function

Definition
A real function $f: \R \to \R$ is said to be simple if it is a linear combination of finitely many characteristic functions:
 * $\displaystyle \phi \left({x}\right) = \sum_{i=1}^n a_i \chi_{E_i} \left({x}\right)$

where each of the sets $E_i \ $ are measurable.