A simple function is a finite sum 
, where the functions 
are characteristic
functions on a set 
.
Another description of a simple function is a function that takes on finitely many
values in its range.
The collection of simple functions is closed under addition and multiplication. In addition, it is easy to integrate a simple function. By approximating
a given function 
by simple functions, the Lebesgue integral of
can be calculated.
