Quasi-ergodicity

Summary

A quasi-ergodic map is a quasi-measure-preserving map of a measure space to itself whose invariant sets are all trivial: null or of null complement. It extends the notion of an ergodic transformation to maps that need not preserve the measure, but only send null sets back to null sets. This is the natural setting of nonsingular ergodic theory, where measures are only known up to equivalence. A quasi-ergodic map cannot be split into two parts of positive measure that the map keeps apart.