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Measurable and nonmeasurable sets with homogeneous sections
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Alexander Kharazishvili
Veröffentlicht/Copyright:
30. Mai 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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Schlagwörter für diesen Artikel
Linear (planar) section of a set;
measurable set;
Fubini's theorem;
nonmeasurable set;
Sierpiński's partition;
iterated integral
Artikel in diesem Heft
- Masthead
- Boundedness of the parametric Marcinkiewicz integral operator and its commutators on generalized Morrey spaces
- Modules that have a supplement in every cofinite extension
- Boundary value problems of statics of the elastic mixture theory
- On grand Lorentz spaces and the maximal operator
- Measurable and nonmeasurable sets with homogeneous sections
- Complexifications of real spaces: General aspects
- Continuous Hu cohomology
- Convergence and existence results for best C-proximity points
- Aspects of slice stability in locale theory
- On the irreducibility of Hurwitz spaces of coverings with two special fibers
- Weighted composition followed by differentiation between weighted Banach spaces of holomorphic functions
