# Article

Full entry | PDF   (0.1 MB)
Keywords:
non-measurable functions; rational automorphism
Summary:
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.
References:
[1] Gelbaum B. R., Olmsted J. M. H.: Counterexamples in Analysis. The Mathesis Series Holden-Day, San Francisco, 1964. MR 0169961
[2] Kharazishvili A. B.: Nonmeasurable Sets and Functions. North-Holland Mathematics Studies, 195, Elsevier Science B.V., Amsterdam, 2004. MR 2067444

Partner of