Almost periodic observable
= Almost periodic observable
{title2=$\{U_T^nf:n\in\mathbb Z\}$}
An $L^2$ observable of an invertible probability <measure-preserving system> is almost periodic when its <Koopman operator> orbit is totally bounded in the global $L^2$ norm. A noninvertible system uses its forward orbit. This is the Hilbert-space dynamical definition, distinguished from uniform almost periodicity for continuous functions of a real variable.