Luzin and Sierpiński sets, some nonmeasurable subsets of the plane and additive properties on the line
arXiv:1406.3062
Abstract
In this paper we shall introduce some nonmeasurable and completely nonmeasurable subsets of the plane with various additional properties, e.g. being Hamel basis, intersecting each line in a strong Luzin / Sierpiński set. Also some additive properties of Luzin and Sierpiński sets and their generalization I-Luzin sets, on the line are investigated.
18 pages