Geodesic
A $Q$-linear automorphism of the reals with non-measurable graph
Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 2, pp. 209-210.

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This note contains a proof of the existence of a one-to-one function $\Theta $ of $\,\mathbb{R}\,$ onto itself with the following properties: $\Theta $ is a rational-linear automorphism of $\mathbb{R}$, and the graph of $\Theta $ is a non-measurable subset of the plane.
DOI : 10.14712/1213-7243.2019.004
Classification : 26A30, 28A05, 28A20
Keywords: non-measurable functions; rational automorphism 
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Scheinberg, Stephen. A $Q$-linear automorphism  of the reals with non-measurable graph. Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 2, pp. 209-210. doi : 10.14712/1213-7243.2019.004. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2019.004/

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