Abstract

In this paper I consider a property of sets in the real line such that every non-empty union of finitely many sets with the property does not contain a set with a positive Lebesgue measure. Selectors of the real numbers \(\mathbb R\) related to any proper dense subgroup of the additive group \((\mathbb R, +)\) as well as cosets of any proper dense subgroup of \((\mathbb R, +)\) possess this property.

中文翻译：

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实线上集合的一些性质和勒贝格可测性

摘要

在这篇论文中，我考虑了实线上集合的一个性质，使得具有该性质的有限多个集合的每个非空并集不包含具有正 Lebesgue 测度的集合。实数选择器\(\mathbb R\)与加性群\((\mathbb R, +)\)的任何真稠密子群以及\((\mathbb R, +)\)拥有这个属性。