ABSTRACT
From what readers already know about Riemann integrals, the Riemann integral is a mapping f which is linear and whose domain is some subspace of the vector space of all bounded functions. In this chapter, the author knows that the Riemann integral satisfies an important idea in analysis called limit interchange. The important topic for us is to consider the class of functions of bounded variation. The author explains similar concepts using abstract measures. Readers are going to find out that functions of bounded variation can also be represented as the difference of two increasing functions and that their classical derivative exists everywhere, except a set of measure zero.
