Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 3 / 26K / a / Solution

A measure-preserving transformation $T$ on a probability space $(X,\mathcal{A},m)$ is ergodic if every invariant event $A\in \mathcal{A}$, meaningup to an $m$-null set, satisfies $m(A)\in \{0,1\}$. Thus the invariant sigma-algebra is trivial modulo null sets.