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  • Print publication year: 2004
  • Online publication date: June 2012

Appendix A - Preliminaries

Summary

The theory of random processes is constructed on a large number of abstractions. These abstractions are necessary to achieve generality with precision while keeping the notation used manageably brief. Students will probably find learning facilitated if, with each abstraction, they keep in mind (or on paper) a concrete picture or example of a special case of the abstraction. From this the general situation should rapidly become clear. Concrete examples and exercises are introduced throughout the book to help with this process.

Set theory

In this section the basic set theoretic ideas that are used throughout the book are introduced. The starting point is an abstract space, or simply a space, consisting of elements or points, the smallest quantities with which we shall deal. This space, often denoted by Ω, is sometimes referred to as the universal set. To describe a space we may use braces notation with either a list or a description contained within the braces { }. Examples are:

  1. [A.0] The abstract space consisting of no points at all, that is, an empty (or trivial) space. This possibility is usually excluded by assuming explicitly or implicitly that the abstract space is nonempty, that is, it contains at least one point.

  2. […]