Almost Erdős sets
Abstract
Abstract A set $S \subseteq \mathbb{R}$ is almost Erdős if, for every $\varepsilon \gt 0$ , there exists a set $E \subseteq \mathbb{R}$ of positive Lebesgue measure such that $\{x \in S : ax+b \notin E\}$ is nonempty for all $|a| \gt \varepsilon$ and $b \in \mathbb{R}$ . In this note, we show that any decreasing null sequence $(x_n)$ with decay rate greater than $1/2$ is an almost Erdős set.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Analytic Number Theory Research
Advanced Topology and Set Theory
Publication details
- Journal / source
- Proceedings of the Edinburgh Mathematical Society
- Pages
- 1–9
- Publication date
- 12 February 2026
- Language
- EN