论文标题
$ \ mathbb {z}^2 \ subset \ mathbb {r}^2 $的子集切片定理
A Marstrand type slicing theorem for subsets of $\mathbb{Z}^2 \subset \mathbb{R}^2$ with the mass dimension
论文作者
论文摘要
我们证明了整数正方形晶格子集的Marstrand型切片定理。这个问题是相应的投影定理的双重，该定理被Glasscock以及利马和莫雷拉（Lima and Moreira）考虑，质量和计数维度应用于$ \ Mathbb {z}^{d} $的子集。在本文中，更普遍地处理了$ 1 $分离的飞机子集，而整数晶格的子集则是特殊情况。我们表明，在这种情况下，自然切片问题在质量维度上是正确的。
We prove a Marstrand type slicing theorem for the subsets of the integer square lattice. This problem is the dual of the corresponding projection theorem, which was considered by Glasscock, and Lima and Moreira, with the mass and counting dimensions applied to subsets of $\mathbb{Z}^{d}$. In this paper, more generally we deal with a subset of the plane that is $1$ separated, and the result for subsets of the integer lattice follow as a special case. We show that the natural slicing question in this setting is true with the mass dimension.
