| Title:
|
A $Q$-linear automorphism of the reals with non-measurable graph (English) |
| Author:
|
Scheinberg, Stephen |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
60 |
| Issue:
|
2 |
| Year:
|
2019 |
| Pages:
|
209-210 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
non-measurable functions |
| Keyword:
|
rational automorphism |
| MSC:
|
26A30 |
| MSC:
|
28A05 |
| MSC:
|
28A20 |
| idZBL:
|
Zbl 07144889 |
| idMR:
|
MR3982468 |
| DOI:
|
10.14712/1213-7243.2019.004 |
| . |
| Date available:
|
2019-08-05T09:46:44Z |
| Last updated:
|
2021-07-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147818 |
| . |
| Reference:
|
[1] Gelbaum B. R., Olmsted J. M. H.: Counterexamples in Analysis.The Mathesis Series Holden-Day, San Francisco, 1964. MR 0169961 |
| Reference:
|
[2] Kharazishvili A. B.: Nonmeasurable Sets and Functions.North-Holland Mathematics Studies, 195, Elsevier Science B.V., Amsterdam, 2004. MR 2067444 |
| . |
