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Publication Date:
March 2010
ISSN:
1572-9176
DOI:
10.1515/GMJ.2008.317

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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Shervashidze, T.

Editorial Board Member: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, J. / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

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On Absolutely Nonmeasurable Sets and Functions

Alexander Kharazishvili1

1A. Razmadze Mathematical Institute, 1, M. Aleksidze St., Tbilisi 0193, Georgia, I. Chavchavadze State University, 32, I. Chavchavadze Ave., Tbilisi 0128, Georgia. E-mail: kharaz2@yahoo.com

Citation Information: Georgian Mathematical Journal. Volume 15, Issue 2, Pages 317–325, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: 10.1515/GMJ.2008.317, March 2010

Publication History:
Received:
2007-10-01
Published Online:
2010-03-10

Abstract

We consider some properties of sets and functions which are measurable (or nonmeasurable) with respect to certain classes of measures. In this context, the notion of an absolutely nonmeasurable set (function) is examined. Sierpiński-Zygmund type functions are constructed having additional properties closely connected with the above-mentioned notion. Also, some small subsets of uncountable commutative groups are discussed whose algebraic sum turns out to be an absolutely nonmeasurable set.

Key words and phrases:: Absolutely nonmeasurable set; absolutely nonmeasurable function; universal measure zero set; extension of measure; generalized Sierpiński set; Sierpiński–Zygmund function

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