The Ergodic Theorem

Tom Wieting
Department of Mathematics, Reed College

Abstract: In 1931, G. D. Birkhoff published the first formal proof of the Ergodic Theorem, which served to justify, in specific contexts of Mathematical Physics, the interchange of time and space averages. Since then, the theorem has played significant roles in probability theory, harmonic analysis, and number theory. The object of this lecture is to sketch a "modern" proof of the theorem and to describe several applications -- in particular, to the theory of continued fractions.