The Erdős similarity problem: a survey
type: Item
instance of: scholarly article
title: The Erdős similarity problem: a survey
zbMATH Open document ID: 1022.28001
author: R. E. Svetic
published in: Real Analysis Exchange
publication date: 2003-01-05T00:00:00Z
review text: A~set~\(E\) of reals is said to be Erdős if there exists a set of positive Lebesgue measure not containing a copy of \(E\), i.e., a set of the form \(x+tE=\{x+te:e\in E\}\) with \(x,t\in\mathbb{R}\), \(t\neq 0\). The Erdős similarity problem asks whether every infinite set is Erdős. The problem can be easily reduced to zero-sequences but the proof is known for only a few special cases not including the geometric sequence \(\{2^{-n}\}_{n=1}^\infty\). The author surveys the known results on Erdős sets and related properties, presents some new results and asks several related questions.
reviewed by: Miroslav Repický
Mathematics Subject Classification ID: 28A05
Mathematics Subject Classification ID: 40A05
zbMATH DE Number: 1848857
zbMATH Keywords: Erdős similarity problem
zbMATH Keywords: Erdős set
zbMATH Keywords: universal set
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1848857