Measure Preserving Systems

Abstract

These notes are from a graduate course given in Spring 2007 at the University of North Carolina at Chapel Hill. A major portion will be published as part of the Springer Online Encyclopedia on Complexity. They provide an introduction to the subject of measure-preserving dynamical systems, discussing the dynamical viewpoint; how and from where measure-preserving systems arise; the construction of measures and invariant measures; some basic constructions within the class of measure-preserving systems; and some mathematical background on conditional expectations, Lebesgue spaces, and disintegrations of measures.