EMIS ELibM Electronic Journals Journal of Applied Analysis
Vol. 2, No. 2, pp. 171-181 (1996)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



On nonmeasurable subgroups of the real line

A.B. Kharazishvili

Institute of Applied Mathematics
University of Tbilisi
University street 2
380043 Tbilisi 43
Republic of Georgia

Abstract: We prove that, for every nonzero $\sigma$-finite measure $\mu$ defined on the real line $R$ and invariant (or quasiinvariant) under all translations of $R$, there exists a subgroup of $R$ nonmeasurable with respect to $\mu$. Some generalizations of this result are discussed, too, and several problems related to them are posed.

Keywords: Real line, invariant measure, quasiinvariant measure, nonmeasurable subgroup, Hamel basis, Ulam matrix,uncountable commutative group, Jonsson group

Classification (MSC2000): 28A05, 28D05

Full text of the article:

Electronic fulltext finalized on: 29 May 2002. This page was last modified: 21 Dec 2002.

© 2002 Heldermann Verlag
© 2002 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition