“real: chapter_13” — 2011/5/22 — 23:35 — page2—#2
13-2 Real Analysis
such as the length of an interval in R and the area of two-dimensional
objects, later on it was associated with curve length, surface area, etc.,
It also gave a far-reaching insight on the differentiability of mono-
tone functions and an extension of the fundamental theorem of integral
calculus.
In fact, both the shortcomings mentioned in the case of Riemann
integration were rectified in this general set up. In this chapter, we shall
give a very brief introduction to this part of real analysis leaving more
general results and extensions to an advanced course in measure theory.
We shall introduce the concept of an outer measure defined on all
subsets of
R and define measurable sets,