Lebesgue integration

Abstract

In Chapter 11, we approached the Riemann integral by first integrating a particularly simple class of functions, namely the piecewise constant functions. Among other things, piecewise constant functions only attain a finite number of values (as opposed to most functions in real life, which can take an infinite number of values). Once one learns how to integrate piecewise constant functions, one can then integrate other Riemann integrable functions by a similar procedure.