chapter  1
16 Pages

Preliminaries

This book is devoted to Lebesgue integration and related topics, a basic part of modern analysis. There are classical and abstract approaches to the integral, and we have chosen the classical one, postponing a more abstract treatment until later in the book. The classical approach is based on the theory of measure (while in some modern treatments, the integral is introduced as a linear functional). Measure can be defined and studied in various spaces, but we will primarily consider n-dimensional Euclidean space, Rn. Aprerequisite, undertaken in this chapter, is a review of elementary notions aboutRn. We have not attempted to present these in a thoroughmanner, but only to list some of the definitions and notation that will be used throughout the book and state some background facts that a reader should know. We assume a knowledge of various properties of the real line R1 and of functions defined on R1 and leave as exercises the proofs of many facts that are either similar to or derivable from their one-dimensional analogues.