Real Analysis Exchange

Absolute Null Subsets of the Plane with Bad Orthogonal Projections

Alexander Kharazishvili

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.

Article information

Source
Real Anal. Exchange, Volume 41, Number 1 (2016), 233-244.

Dates
First available in Project Euclid: 29 March 2017