O'Reilly logo

A Signal Theoretic Introduction to Random Processes by Roy M. Howard

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

2 BACKGROUND: MATHEMATICS

2.1 INTRODUCTION

This chapter details relevant mathematical theory, and mathematical results, to provide the basis for analysis in subsequent chapters and to ensure a coherent and systematic development of material. A summary of mathematical notation is detailed in the notation table in the reference section at the end of the book.

A basic introduction to set theory, and function theory, is provided, and this is followed by an introduction to measure theory. Two types of measure are considered. The first, Lebesgue measure, underpins Lebesgue integration, and this is fundamental to signal theory, which is discussed in Chapter 3. The second, Lebesgue–Stieltjes measure, provides the basis for Lebesgue–Stieltjes integration. Lebesgue–Stieltjes integration underpins Cramer’s representation of a signal, which is discussed in Chapter 3. The discussion, in general, complements that of Howard (2002, ch. 2).

2.2 SET THEORY

2.2.1 Basic Definitions

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required