论文标题
一组完整的措施避免了cantor套装
Sets of full measure avoiding Cantor sets
论文作者
论文摘要
关于ERD \ H OS相似性问题（表明，对于任何无限集$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a），我们给出了一些新的无限集示例，这些示例是不通用的，即满足上述猜测。这些是对称的Cantor集合$ C $，可能很薄：定义Cantor套件的$ n $ Then Generation间隔的长度几乎呈指数增长。此外，我们实现了构建一个集合，而不仅是积极的措施，还可以构建\ textit {完整度量}不包含$ c $的任何仿制副本。我们的方法是概率。
In relation to the Erd\H os similarity problem (show that for any infinite set $A$ of real numbers there exists a set of positive Lebesgue measure which contains no affine copy of $A$) we give some new examples of infinite sets which are not universal in measure, i.e. they satisfy the above conjecture. These are symmetric Cantor sets $C$ which can be quite thin: the length of the $n$-th generation intervals defining the Cantor set is decreasing almost doubly exponentially. Further, we achieve to construct a set, not just of positive measure, but of \textit{full measure} not containing any affine copy of $C$. Our method is probabilistic.
