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Georgian Mathematical Journal

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

Editorial Board: 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, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

Online
ISSN
1572-9176
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Volume 19, Issue 2

Issues

Measurable and nonmeasurable sets with homogeneous sections

Alexander Kharazishvili
  • A. Razmadze Mathematical Institute of I. Javakhishvili Tbilisi State University, 2 University Str., Tbilisi 0186, Georgia
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Published Online: 2012-05-30 | DOI: https://doi.org/10.1515/gmj-2012-0009

Abstract.

The paper is concerned with measurable and nonmeasurable subsets of the unit square (unit cube) whose linear (planar) sections have constant linear (planar) Lebesgue measure. Some properties of such subsets are studied and their connections with the existence of iterated integrals are pointed out.

Keywords: Linear (planar) section of a set; measurable set; Fubini's theorem; nonmeasurable set; Sierpiński's partition; iterated integral

About the article

Received: 2011-05-24

Published Online: 2012-05-30

Published in Print: 2012-06-01


Citation Information: Georgian Mathematical Journal, Volume 19, Issue 2, Pages 247–258, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2012-0009.

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© 2012 by Walter de Gruyter Berlin Boston.Get Permission

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