On absolutely nonmeasurable homomorphisms of commutative groups

A. Kharazishvili

doi:10.1556/sscmath.50.2013.3.1242

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 50: Issue 3

On absolutely nonmeasurable homomorphisms of commutative groups

Author:

A. Kharazishvili

A. Kharazishvili A. Razmadze Mathematical Institute University Street, 2 Tbilisi 0186 Georgia

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Pages:: 287–295

Online Publication Date:: 08 Oct 2013

Publication Date:: 01 Sep 2013

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.50.2013.3.1242

Keywords:: Primary 28A20; 28D05; 22B99; Commutative group; Kulikov’s theorem; absolutely nonmeasurable homomorphism; universal measure zero set

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We give a characterization of all those commutative groups which admit at least one absolutely nonmeasurable homomorphism into the real line (or into the one-dimensional torus). These are exactly those commutative groups (G, +) for which the quotient group G/G₀ is uncountable, where G₀ denotes the torsion subgroup of G.

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

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Studia Scientiarum Mathematicarum Hungarica
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