a Measure that is preserved by some Function

We say that the function $f: X \rightarrow X$ preserves a measure $\mu$ on $(X\mathcal{B})$, if $\mu(f^{-1} B) = \mu(B)$, for all $B \in \mathcal{B}$. The function is then said to be $\mu$-preserving, or $\mu$ is said to be $f$-invariant.

https://en.wikipedia.org/wiki/Invariant_measure