Abstract
Under Martin’s Axiom, it is proved that there exists an absolute null subset of the Euclidean plane $\mathbb{R}^2$, the orthogonal projections of which on all straight lines in $\mathbb{R}^2$ are absolutely nonmeasurable. A similar but weaker result holds true within the framework of ZFC set theory.
Citation
Alexander Kharazishvili. "Absolute Null Subsets of the Plane with Bad Orthogonal Projections." Real Anal. Exchange 41 (1) 233 - 244, 2016.
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