@article{727a19de8e714860bdca879589ffc737,
title = "Measure complexity and M{\"o}bius disjointness",
abstract = "In this paper, the notion of measure complexity is introduced for a topological dynamical system and it is shown that Sarnak's M{\"o}bius disjointness conjecture holds for any system for which every invariant Borel probability measure has sub-polynomial measure complexity. We then apply this result to a number of situations, including certain systems whose invariant measure don't all have discrete spectrum.",
author = "Wen Huang and Zhiren Wang and Xiangdong Ye",
note = "Funding Information: Acknowledgments. We thank El Abdalaoui for bringing our attention to the work of [38], and for informing us the question of M{\"o}bius Orthogonality for K(Z). We thank the referee for detailed reading and helpful comments, especially for informing us of other authors{\textquoteright} proofs of Theorems 1.2 and 1.6. W. Huang and X. Ye are supported by NNSF of China (11225105, 11431012, 11571335). Z. Wang was supported by NSF (DMS-1501095). Publisher Copyright: {\textcopyright} 2019",
year = "2019",
month = apr,
day = "30",
doi = "10.1016/j.aim.2019.03.007",
language = "English (US)",
volume = "347",
pages = "827--858",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
}