Luzin and Sierpiński sets, some nonmeasurable subsets of the plane and additive properties on the line
Marcin Michalski,
Szymon Żeberski
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 super Luzin/Sierpiński set. Also some additive properties of Luzin and Sierpiński sets and their generalization, I-Luzin sets, on the line are investigated.
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