Ergodic Theory - Ergodic Transformations

Ergodic theory is often concerned with ergodic transformations.

Let T: X → X be a measure-preserving transformation on a measure space (X, Σ, μ), with μ(X) = 1. A measure-preserving transformation T as above is ergodic if for every E in Σ with T−1(E) = E, then either μ(E) = 0 or μ(E) = 1.