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Approximating elements of the middle third Cantor set with dyadic rationals
Let C be the middle third Cantor set and μ be the log 2/log 3 -dimensional Hausdorff measure restricted to C. In this paper we study approximations of elements of C by dyadic rationals.
Our main result implies that for μ almost every x ∈ C we have
(mathematical equation here)
This improves upon a recent result of Allen, Chow, and Yu which gives a sub-logarithmic improvement over the trivial approximation rate.
Funding
Overlapping iterated function systems: New approaches and breaking the super-exponential barrier
Engineering and Physical Sciences Research Council
Find out more...History
School
- Science
Department
- Mathematical Sciences
Published in
Israel Journal of MathematicsPublisher
SpringerVersion
- AM (Accepted Manuscript)
Publisher statement
This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/[insert DOI]Acceptance date
2023-01-29ISSN
0021-2172eISSN
1565-8511Publisher version
Language
- en
