## Introduction to the

First Billingsley Lecture on Probability Theory

Welcome to the first Billingsley Lecture on Probability Theory. This
is the first in what will be an annual series of special lectures
to commemorate the contributions of Patrick
Billingsley to the field of probability theory and to the University
of Chicago, where Pat spent nearly all of his academic career, from
1958 until his retirement in 1994.

Pat Billingsley was a man of diverse talents: he excelled not only as
a scholar and a teacher but also as a writer, an actor, and even a black
belt in judo. Pat is remembered for his research in weak convergence,
in ergodic theory and its connections with information theory, in
probabilistic number theory, and as the inventor of the "Billingsley
dimension" of a measure. He advised a number of Ph.D. students
during his years on the UC faculty, several of whom went on to
distinguished careers in mathematics, including Rabi Bhattacharya and
Richard Gundy. He played leading roles in more than 20 productions of
the Court Theater, and also appeared in a number of movies and
television shows. Pat once remarked to me that he suspected he was one of the few
people alive whose Erdös number and his Kevin Bacon
number summed to less than ten. (He did not know of Wendelin Werner
another distinguished probabilist who like Pat has an Erdös-Bacon number
of 6. In fact, Pat shares 12th place in this category, along with Werner,
Richard Feynman, John Nash, and Tom Lehrer.)

But what we in the fields of probability and statistics mainly
remember Pat for are his superb monographs and textbooks on weak
convergence, ergodic theory and information, inference for Markov
chains, and the measure-theoretic foundations of probability. These
books are all models of mathematical exposition, and "Probability and
Measure" remains a widely used and frequently cited graduate textbook. A
generation of probabilists and statisticians in the United States learned about the
measure-theoretic underpinnings of probability from this book.

Pat would have been pleased to be honored by a lecture series such as
this, and especially proud that the first lecture would be delivered
by Raghu Varadhan.