Almost Erdős sets

Berdellima, Arian

doi:10.1017/S0013091526101370

Almost Erdős sets

2026-02-01

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Berdellima, Arian *

DOI：10.1017/S0013091526101370

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A set $S \subseteq \mathbb{R}$ is almost Erd & odblac;s 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 Erd & odblac;s set.

Keywords:

almost Erd & odblac

s sets

decreasing null sequences

Lebesgue measure

Hausdorff dimension

additive combinatorics

Almost Erdős sets

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