A simple function is a finite sum sum_i a_i χ_(A_i), where the functions χ_(A_i) are characteristic functions on a set A. 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 f by simple functions, the Lebesgue integral of f can be calculated.

characteristic function | Lebesgue integrable | Lebesgue integral | set