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2016 Absolute Null Subsets of the Plane with Bad Orthogonal Projections
Alexander Kharazishvili
Real Anal. Exchange 41(1): 233-244 (2016).


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.


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Alexander Kharazishvili. "Absolute Null Subsets of the Plane with Bad Orthogonal Projections." Real Anal. Exchange 41 (1) 233 - 244, 2016.


Published: 2016
First available in Project Euclid: 29 March 2017

zbMATH: 1384.28003
MathSciNet: MR3511944

Primary: 28A05 , 28D05
Secondary: 03E25

Keywords: Absolute null set , Bernstein set , generalized Luzin set , Hamel basis

Rights: Copyright © 2016 Michigan State University Press

Vol.41 • No. 1 • 2016
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