文章基本信息

标题：Fractal Intersections and Products via Algorithmic Dimension
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作者：Neil Lutz
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：83
页码：58:1-58:12
DOI：10.4230/LIPIcs.MFCS.2017.58
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Algorithmic dimensions quantify the algorithmic information density of individual points and may be defined in terms of Kolmogorov complexity. This work uses these dimensions to bound the classical Hausdorff and packing dimensions of intersections and Cartesian products of fractals in Euclidean spaces. This approach shows that a known intersection formula for Borel sets holds for arbitrary sets, and it significantly simplifies the proof of a known product formula. Both of these formulas are prominent, fundamental results in fractal geometry that are taught in typical undergraduate courses on the subject.
关键词：algorithmic randomness; geometric measure theory; Hausdorff dimension; Kolmogorov complexity