TABLE OF CONTENTS This appendix provides a brief overview of the main concepts in probability theory, random variables, and random processes that are used throughout the book. More detailed treatments of these broad and deep topics, along with proofs for the properties stated in this appendix, can be found in [1; 2; 3; 4; 5; 6; 7; 8].
Probability theory provides a mathematical characterization for random events. Such events are defined on an underlying probability space ( ?, 
, p( )). The probability space consists of a sample space ? of possible outcomes for random events; a set of random events , where each A ? is a subset of ?; and a probability measure p( ) defined on these subsets. Thus, is a set of sets, and the probability measure p(A) is defined for every set A ? . A probability space requires that the set be a ?-field. Intuitively, a set of sets is a ?-field if it contains all intersections, unions, and complements of its elements. [1] More precisely, is a ?-field if: the set of all possible outcomes ? is one of the sets inE; a set A ? implies that A c ? ; and, for any sets A 1, A 2, with A i ? , we have 
. The set must be a ?-field in order...
