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Measurable and nonmeasurable sets with homogeneous sections
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Alexander Kharazishvili
Published/Copyright:
May 30, 2012
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
Received: 2011-05-24
Published Online: 2012-05-30
Published in Print: 2012-June
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
Linear (planar) section of a set;
measurable set;
Fubini's theorem;
nonmeasurable set;
Sierpiński's partition;
iterated integral
Articles in the same Issue
- Masthead
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- Modules that have a supplement in every cofinite extension
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- Measurable and nonmeasurable sets with homogeneous sections
- Complexifications of real spaces: General aspects
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