The map $F$ is a <measure-preserving transformation> when
$$
\boxed{\omega(F^{-1}(B))=\omega(B)}
$$
for every <Borel set> $B$, equivalently $F_*\omega=\omega$. In this case its <Koopman operator> is an <isometry> on $L^2(\omega)$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 358 / 3 / a / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-358/3/a/ii/solution