This book has been written for several reasons, not all of which are academic. This material was
for many years the ﬁrst half of a book in progress on information and ergodic theory. The intent
was and is to provide a reasonably selfcontained advanced treatment of measure theory, probability
theory, and the theory of discrete time random processes with an emphasis on general alphabets
and on ergodic and stationary properties of random processes that might be neither ergodic nor
stationary. The intended audience was mathematically inclined engineering graduate students and
visiting scholars who had not had formal courses in measure theoretic probability. Much of the
material is familiar stuﬀ for mathematicians, but many of the topics and results have not previously
appeared in books.
