Measure and Integral

Abstract

Measure theory is a branch of mathematics. Length, area, volume and weight are instances of measure concept. The emphasis in this chapter is mainly on the concept of measure, Borel set, measurable function, Lebesgue integral, Lebesgue-Stieltjes integral, monotone class theorem, Carathéodory extension theorem, measure continuity theorem, product measure theorem, monotone convergence theorem, Fatou’s lemma, Lebesgue dominated convergence theorem, and Fubini theorem. The main results in this chapter are well-known. For this reason the credit references are not given. This chapter can be omitted by the readers who are familiar with the basic concepts and theorems of measure and integral.