# Tag Info

Question about probability spaces $(X,\mathcal B,\mu)$ with a measurable map $T\colon X\to X$ preserving the measure, that is $\mu(T^{—1}A)=\mu(A)$ for all $A$ measurable.
Given a measure space $(X,\mathcal B,\mu)$, a measure-preserving transformation on $X$ is a measurable map $T\colon X\to X$ preserving the measure $\mu$. This means that $\mu(T^{—1}A)=\mu(A)$ for all measurable sets $A\subset X$.