On Möbius disjointness for infinite measure-preserving transformations (Q6589622)

The property of `Möbius disjointess', asymptotic orthogonality of the classical Möbius function to an observable on a topological dynamical system, is studied in the setting of infinite measure-preserving systems. Disjointness is shown to not hold at almost all points in the class of continuous bounded integrable observables for an ergodic system, and a large class of rank-one infinite measure preserving systems are found for which periodic continuous observables do satisfy Möbius disjointness.