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:
 * $$\phi \left({x}\right) = \sum_{i=1}^n a_i \chi_{E_i} \left({x}\right)$$

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