论文标题
宏观Hausdorff维度的潜在方法和投影定理
Potential method and projection theorems for macroscopic Hausdorff dimension
论文作者
论文摘要
Barlow和Taylor引入了集合E $ \子集$ r D的宏观Hausdorff尺寸dim h（e），以量化无界（可能是离散的，可能是离散的）的“分形”行为。然后，我们应用这种方法来获取类似Marstrand的投影定理：给定$ [0，2 $π$]的e $ \ subset $ r 2，几乎每个$θ$ \ \ in $θ$ \ \]，E上E上E上的E投影在0 the Angle $θ$的直线上，$θ$具有尺寸等于dimension dim Min（DIM H（e），1），1），1）。
The macroscopic Hausdorff dimension Dim H (E) of a set E $\subset$ R d was introduced by Barlow and Taylor to quantify a "fractal at large scales" behavior of unbounded, possibly discrete, sets E. We develop a method based on potential theory in order to estimate this dimension in R d. Then, we apply this method to obtain Marstrand-like projection theorems: given a set E $\subset$ R 2 , for almost every $θ$ $\in$ [0, 2$π$], the projection of E on the straight line passing through 0 with angle $θ$ has dimension equal to min(Dim H (E) , 1).
