Abstract
Let μ be a self-similar measure supported on a self-similar set K with the open set condition. For x∈K, let A(D(x)) be the set of accumulation points of Dr(x)=logμ(B(x,r))logr as r↘0. In this paper, we show that for any closed non-singleton subinterval I⊂R, the set of points x for which the set A(D(x)) equals I is either empty or residual.
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.
