发表机构
Ningbo University（宁波大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对相邻比值有下界的正零序列，通过适配有限树构造方法，证明存在不含其非平凡仿射拷贝的正测度紧集，还可推广至任意可数序列族的情形。
AI 中文摘要
设$(a_n)$为满足$\liminf_{n\to\infty}a_{n+1}/a_n>0$的正零序列。对每个$\eta>0$，我们构造一个勒贝格测度大于$1-\eta$的紧集$E\subset[0,1]$，该集合不含$\{a_n:n\ge1\}$的非平凡仿射拷贝，且未施加任何单调性条件。证明过程将针对几何序列的有限树构造方法适配至由具有双侧比值界的子序列选取的网格，我们还能为任意指定的可数序列族构造这样的集合，使得每个仿射拷贝都遗漏无穷多个不同点。
英文摘要
Let $(a_n)$ be a positive null sequence with $\liminf_{n\to\infty}a_{n+1}/a_n>0$. For every $η>0$, we construct a compact set $E\subset[0,1]$ with Lebesgue measure greater than $1-η$ containing no nontrivial affine copy of $\{a_n:n\ge1\}$. No monotonicity is assumed. The proof adapts a finite-tree construction for geometric sequences to grids chosen from a subsequence with two-sided ratio bounds. We also obtain one such set for any prescribed countable family of sequences, with infinitely many distinct points omitted from every affine copy.
Comments10 pages
