The material in this book breaks up into three main parts. Chapters 1 to 3
cover essentially introductory and preparatory material. Chapter 1 contains
an elementary discussion of random fields and some probability. Chapter 2 is
devoted to the spectral representation of homogeneous fields. This material
generally differs only in minor notational aspects from the spectral theory of
stationary processes on the real line, and so very few proofs are given. Later in
the book a variety of regularity conditions needs to be imposed on the sample
functions of fields for certain results to be meaningful, and Chapter 3 is devoted
to examining when these regularity conditions are satisfied. Also included in
Chapter 3 is Garsia's development of the Karhunen-Loeve expansion for
Gaussian fields.