Luzin and Sierpi\'nski sets, some nonmeasurable subsets of the plane and additive properties on the line
classification
🧮 math.GN
keywords
lineluzinnonmeasurablenskipropertiessetssierpisome
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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 / Sierpi\'nski set. Also some additive properties of Luzin and Sierpi\'nski sets and their generalization I-Luzin sets, on the line are investigated.
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