Measurable Sensitivity

Jennifer James, Thomas Koberda, Kathryn Lindsey, Cesar E. Silva, Peter Speh

Published 2006-12-17, updated 2006-12-19Version 2

We introduce the notion of measurable sensitivity, a measure-theoretic version of the condition of sensitive dependence on initial conditions. It is a consequence of light mixing, implies a transformation has only finitely many eigenvalues, and does not exist in the infinite measure-preserving case. Unlike the traditional notion of sensitive dependence, measurable sensitivity carries up to measure-theoretic isomorphism, thus ignoring the behavior of the function on null sets and eliminating dependence on the choice of metric.