Recent progress in ergodic theory

Abstract

In 1948, at the November meeting of the Society in Chicago, I delivered an address entitled Measurable transformations. In the twelve years that have elapsed since then, ergodic theory (of which the theory of measurable transformations is the greatest part) has been spectacularly active. The purpose of today's address is to report some of the developments of those twelve years ; its title might well have been Measurable transformations revisited. The subjects I chose for this purpose are: some new ergodic theorems, information theory and its connection with ergodic theory, and the problem of invariant measure.