Dirichlet sets and Erdos-Kunen-Mauldin theorem
| dc.creator | Elias, Peter | |
| dc.date | 2007-12-13 | |
| dc.date.accessioned | 2026-07-07T08:48:59Z | |
| dc.date.available | 2026-07-07T08:48:59Z | |
| dc.description | By 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.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/0712.2112 | |
| dc.identifier | http://arxiv.org/abs/0712.2112 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144144 | |
| dc.subject | General Topology | |
| dc.subject | 28A05; 54H05; 54H11 | |
| dc.title | Dirichlet sets and Erdos-Kunen-Mauldin theorem | |
| dc.type | text |