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arXiv · 1911.05915

Hausdorff Measures, Dyadic Approximations and Dobi\'nski Set

Alberto Dayan·José L. Fernández·María J. González
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Abstract

Dobi\'nski set $\mathcal{D}$ is an exceptional set for a certain infinite product identity, whose points are characterized as having exceedingly good approximations by dyadic rationals. We study the Hausdorff dimension and logarithmic measure of $\mathcal{D}$ by means of the Mass Transference Principle and by the construction of certain appropriate Cantor-like sets, termed willow sets, contained in $\mathcal{D}$.

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Alberto Dayan, José L. Fernández, María J. González. 2019-11-14. Hausdorff Measures, Dyadic Approximations and Dobi\'nski Set. https://arxiv.org/abs/1911.05915

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