Orthogonal projections of discretized sets

IF 1.1 4区 数学 Q1 MATHEMATICS Journal of Fractal Geometry Pub Date : 2017-10-02 DOI:10.4171/jfg/92
Weikun He
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引用次数: 32

Abstract

We generalize Bourgain's discretized projection theorem to higher rank situations. Like Bourgain's theorem, our result yields an estimate for the Hausdorff dimension of the exceptional sets in projection theorems formulated in terms of Hausdorff dimensions. This estimate complements earlier results of Mattila and Falconer.
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离散集的正交投影
我们将布尔甘的离散投影定理推广到高阶情形。与布尔甘定理一样,我们的结果给出了用Hausdorff维数表示的投影定理中异常集的Hausdorff维数的估计。这一估计补充了Mattila和Falconer早先的结果。
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