Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/some-property-of-sets-in-the-real-line-and-the-lebesgue-measurability-Z1jvlEGC0r
References (8)
-
M. Kysiak (2009)
Central European Journal of Mathematics Bernstein sets with algebraic properties -
A. Kharazishvili (2011)
Measurability Properties of Vitali SetsThe American Mathematical Monthly, 118
-
(2001)
On translations of subsets of the3 real line, -
M. Kysiak (2009)
Bernstein sets with algebraic propertiesCent. Eur. J. Math., 7
-
J. Cichon (2001)
10.1090/S0002-9939-01-06224-4Proc. Amer. Math. Soc., 130
-
V. Chatyrko (2019)
Semigroups of pathological setsGeorgian Mathematical Journal, 26
-
(2021)
Sul problema della mesura dei gruppi di punti di una retta (Bologna, 1905) -
J. C. Oxtoby (1971)
10.1007/978-1-4615-9964-7
- Publisher
- Springer Journals
- Copyright
- Copyright © Pleiades Publishing, Ltd. 2021
- ISSN
- 2070-0466
- eISSN
- 2070-0474
- DOI
- 10.1134/s2070046621040075
- Publisher site
- See Article on Publisher Site
Abstract
In this paper I consider a property of sets in the real line such that every non-empty union of finitely many sets with the property does not contain a set with a positive Lebesgue measure. Selectors of the real numbers \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathbb R$$\end{document} related to any proper dense subgroup of the additive group \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(\mathbb R, +)$$\end{document} as well as cosets of any proper dense subgroup of \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(\mathbb R, +)$$\end{document} possess this property.
Journal
P-Adic Numbers, Ultrametric Analysis, and Applications – Springer Journals
Published: Oct 1, 2021
Keywords: measurable sets in the Lebesgue sense; dense subgroups of the real numbers; selectors of the real numbers related to a dense subgroup