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引用次数: 0
摘要
我们考虑的是可整型集合 Γ 的平面贝西科维奇集合的豪斯多夫维度，即在每个方向上都包含 Γ 的旋转副本的集合。我们证明，对于一大类 Cantor 集 C 和建立在 C 上的 Cantor 图 Γ，任何 Γ-Besicovitch 集的 Hausdorff 维度必须至少为 ，其中 。
Hausdorff dimension of Besicovitch sets of Cantor graphs
We consider the Hausdorff dimension of planar Besicovitch sets for rectifiable sets Γ, that is, sets that contain a rotated copy of Γ in each direction. We show that for a large class of Cantor sets C and Cantor-graphs Γ built on C, the Hausdorff dimension of any Γ-Besicovitch set must be at least , where .
期刊介绍：
Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.
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