Abstract
The paper is devoted to a study of product recurrence. First, we prove that notions of ℱps-PR and ℱpubd-PR are exactly the same as product recurrence, completing that way results of [P. Dong, S. Shao, X. Ye, Product recurrent properties, disjointness and weak disjointness, Israel J. Math. 188 (1) (2012) 463–507], and consequently, extending the characterization of return times of distal points which originated from the works of Furstenberg. We also study the structure of the set of return times of weakly mixing sets. As a consequence, we obtain new sufficient conditions for ℱs-PR and also find a short proof that weakly mixing systems are disjoint with all minimal distal systems (in particular, our proof does not involve Furstenberg’s structure theorem of minimal distal systems).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
