On sets of Vitali’s type
HTML articles powered by AMS MathViewer
- by J. Cichoń, A. Kharazishvili and B. Węglorz PDF
- Proc. Amer. Math. Soc. 118 (1993), 1243-1250 Request permission
Abstract:
We consider the classical Vitali’s construction of nonmeasurable subsets of the real line $\mathbb {R}$ and investigate its analogs for various uncountable subgroups of $\mathbb {R}$. Among other results we show that if $G$ is an uncountable proper analytic subgroup of $\mathbb {R}$ then there are Lebesgue measurable and Lebesgue nonmeasurable selectors for $\mathbb {R}/G$.References
- P. Erdős, K. Kunen, and R. Daniel Mauldin, Some additive properties of sets of real numbers, Fund. Math. 113 (1981), no. 3, 187–199. MR 641304, DOI 10.4064/fm-113-3-187-199 D. Fremlin, Cichon’s diagram, Sem. d’Initiation à l’Analyse (G. Choquet, M. Rogalski, J. Saint-Raymond, eds.), Univ. Pierre et Marie Curie, Paris 23 (1983-84), 5.01-5.12.
- A. B. Kharazishvili, Invariantnye prodolzheniya mery lebega, Tbilis. Gos. Univ., Tbilisi, 1983 (Russian). MR 705928
- Gabriel Mokobodzki, Ensembles à coupes dénombrables et capacités dominées par une mesure, Séminaire de Probabilités, XII (Univ. Strasbourg, Strasbourg, 1976/1977) Lecture Notes in Math., vol. 649, Springer, Berlin, 1978, pp. 491–508 (French). MR 520024
- Jan Mycielski, Independent sets in topological algebras, Fund. Math. 55 (1964), 139–147. MR 173645, DOI 10.4064/fm-55-2-139-147
- Jan Mycielski, Algebraic independence and measure, Fund. Math. 61 (1967), 165–169. MR 224762, DOI 10.4064/fm-61-2-165-169
- John C. Oxtoby, Measure and category, 2nd ed., Graduate Texts in Mathematics, vol. 2, Springer-Verlag, New York-Berlin, 1980. A survey of the analogies between topological and measure spaces. MR 584443, DOI 10.1007/978-1-4684-9339-9
- Janusz Pawlikowski, Small subset of the plane which almost contains almost all Borel functions, Pacific J. Math. 144 (1990), no. 1, 155–160. MR 1056671, DOI 10.2140/pjm.1990.144.155
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 118 (1993), 1243-1250
- MSC: Primary 28B20; Secondary 03C62, 03E35, 54C65
- DOI: https://doi.org/10.1090/S0002-9939-1993-1151809-7
- MathSciNet review: 1151809