ABSTRACT
This chapter extends the concept of integral from non-negative real valued measurable functions to real or complex valued measurable functions. Also, it proves one of the most important theorems in the theory of measure and integration, namely, the dominated convergence theorem, and presents many important and useful consequences of this theorem. The chapter discusses Lp spaces and Hölder’s and Minkowski’s inequalities as well as fundamental theorems of Lebesgue integration. Every monotonically increasing function φ:[a,b]→R is of bounded variation and its total variation is φ(b) - φ(a) and every characteristic function on [a, b] is of bounded variation.
