omg I just took a look at Apostol's "Mathematical Analysis"

InquilineKea
Wed, 11 Jul 2007 00:12:14 +0000

The Riemann integral .f(x)dx, as developed in Chapter 7, is well motivated,
simple to describe, and serves all the needs of elementary calculus. However, this
integral does not meet all the requirements of advanced analysis. An extension,
called the Lebesgue integral, is discussed in this chapter. It permits more general
functions as integrands, it treats bounded and unbounded functions simultaneously,
and it enab]es us to replace the interval [a, b] by more general sets.



I love this explanation :)