通过多尺度分析的Besicovitch投影定理的定量版本
A quantitative version of the Besicovitch projection theorem via multiscale analysis
摘要：
通过使用多尺度分析，我们建立定量版本的贝西科维奇投影定理（几乎每一个投影的纯粹不可求长集在平面上的有限长度的措施零）和一个标准的同伴的结果，即任何平面集至少有两个投影的措施零是纯粹不可求长。我们说明了这些结果，提供了一个明确的（但弱）的平均投影的$n^{th}$代产品康托尔集的上界。
英文摘要：
By using a multiscale analysis, we establish quantitative versions of the Besicovitch projection theorem (almost every projection of a purely unrectifiable set in the plane of finite length has measure zero) and a standard companion result, namely that any planar set with at least two projections of measure zero is purely unrectifiable. We illustrate these results by providing an explicit (but weak) upper bound on the average projection of the $n^{th}$ generation of a product Cantor set.
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