Invariant set of a measure-preserving transformation
= Invariant set of a measure-preserving transformation
= Invariant set
{synonym}
A measurable set $A$ satisfying $T^{-1}A=A$, or equality modulo null sets in the measure-theoretic convention. These sets form a $\sigma$-algebra, and an <ergodic measure-preserving transformation> gives each invariant set probability zero or one.