Mobius disjointness for topological models of ergodic measure-preserving systems with quasi-discrete spectrum

By using a decomposition result for ergodic measure-preserving system with quasi-discrete spectrum, we prove that a generic point of an ergodic quasi-discrete spectrum measure in a topological dynamical system satisfies the required disjointness condition in Sarnak's Mobius Disjointness Conjecture. As a direct application, we have that Sarnak's Mobius Disjointness Conjecture holds for any topological model of an ergodic measure-preserving system with quasi-discrete spectrum. (C) 2018 Elsevier Inc. All rights reserved.