豪斯多夫测度，二进逼近和Dobiński集

IF 0.6 Q3 MATHEMATICS

Illinois Journal of Mathematics Pub Date : 2019-11-14 DOI:10.1215/00192082-9082098

Alberto Dayan, Jos'e L. Fern'andez, Mar'ia J. Gonz'alez

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引用次数: 2

摘要

Dobinski集$\mathcal{D}$是某无穷积恒等式的例外集，其点具有极好的对进有理近似。利用传质原理和构造包含在$\mathcal{D}$中的适当的类cantor集(柳树集)，研究了$\mathcal{D}$的Hausdorff维数和对数测度。

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Hausdorff measures, dyadic approximations, and the Dobiński set

Dobinski 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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来源期刊

Illinois Journal of Mathematics 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

期刊介绍： IJM strives to publish high quality research papers in all areas of mainstream mathematics that are of interest to a substantial number of its readers. IJM is published by Duke University Press on behalf of the Department of Mathematics at the University of Illinois at Urbana-Champaign.