强Marstrand定理与超平面子集所构成集合的维数
Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes
摘要：
我们提出强版本的Marstrand的投影定理和其他相关定理。例如，如果E是一个正的有限s维Hausdorff测度的平面集，则存在一个勒贝格测度0的方向集X，使得E的任何正s维测度子集F在X外方向的任何直线上的投影具有豪斯多夫维数min（1，s），即例外方向集与F无关。使用对偶这导致的结果集的维度相交家庭的线或超平面在积极的勒贝格测度。
英文摘要：
We present strong versions of Marstrand's projection theorems and other related theorems. For example, if E is a plane set of positive and finite s-dimensional Hausdorff measure, there is a set X of directions of Lebesgue measure 0, such that the projection onto any line with direction outside X, of any subset F of E of positive s-dimensional measure, has Hausdorff dimension min(1,s), i.e. the set of exceptional directions is independent of F. Using duality this leads to results on the dimension of sets that intersect families of lines or hyperplanes in positive Lebesgue measure.
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