Dirichlet sets and Erdos-Kunen-Mauldin theorem

dc.creatorElias, Peter
dc.date2007-12-13
dc.date.accessioned2026-07-07T08:48:59Z
dc.date.available2026-07-07T08:48:59Z
dc.descriptionBy a theorem proved by Erdos, Kunen and Mauldin, for any nonempty perfect set $P$ on the real line there exists a perfect set $M$ of Lebesgue measure zero such that $P+M=\mathbb{R}$. We prove a stronger version of this theorem in which the obtained perfect set $M$ is a Dirichlet set. Using this result we show that for a wide range of familes of subsets of the reals, all additive sets are perfectly meager in transitive sense. We also prove that every proper analytic subgroup $G$ of the reals is contained in an F-sigma set $F$ such that $F+G$ is a meager null set.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/0712.2112
dc.identifierhttp://arxiv.org/abs/0712.2112
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144144
dc.subjectGeneral Topology
dc.subject28A05; 54H05; 54H11
dc.titleDirichlet sets and Erdos-Kunen-Mauldin theorem
dc.typetext

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