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Measurability properties of certain paradoxical subsets of the real line
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Mariam Beriashvili
Published/Copyright:
January 14, 2016
Abstract
The paper deals with the measurability properties of some classical subsets of the real line ℝ having an extra-ordinary descriptive structure: Vitali sets, Bernstein sets, Hamel bases, Luzin sets and Sierpiński sets. In particular, it is shown that there exists a translation invariant measure μ on ℝ extending the Lebesgue measure and such that all Sierpiński sets are measurable with respect to μ.
Keywords: Invariant measure; quasi-invariant measure; Vitali set; Bernstein set; Hamel basis; Luzin set; Sierpiński set
Funding source: Shota Rustaveli National Science Foundation
Award Identifier / Grant number: 31/25
Received: 2014-4-13
Revised: 2014-10-31
Accepted: 2014-11-5
Published Online: 2016-1-14
Published in Print: 2016-3-1
© 2016 by De Gruyter
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Articles in the same Issue
- Frontmatter
- The annihilating-ideal graph of a lattice
- On derivations and commutativity of prime rings with involution
- On the traces of certain classes of permuting mappings in rings
- Measurability properties of certain paradoxical subsets of the real line
- Some classical Tauberian theorems for (C,1,1,1) summable triple sequences
- Approximation by trigonometric polynomials in the framework of variable exponent grand Lebesgue spaces
- Irrationality measures for almost periodic continued fractions
- Elementary volume and measurability properties of additive functions
- On (n+1)-Hom-Lie algebras induced by n-Hom-Lie algebras
- Generalization of Hermite–Hadamard type inequalities for n-times differentiable functions through preinvexity
- Nonlinear iterative algorithms for quasi contraction mapping in modular space
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Keywords for this article
Invariant measure;
quasi-invariant measure;
Vitali set;
Bernstein set;
Hamel basis;
Luzin set;
Sierpiński set
Articles in the same Issue
- Frontmatter
- The annihilating-ideal graph of a lattice
- On derivations and commutativity of prime rings with involution
- On the traces of certain classes of permuting mappings in rings
- Measurability properties of certain paradoxical subsets of the real line
- Some classical Tauberian theorems for (C,1,1,1) summable triple sequences
- Approximation by trigonometric polynomials in the framework of variable exponent grand Lebesgue spaces
- Irrationality measures for almost periodic continued fractions
- Elementary volume and measurability properties of additive functions
- On (n+1)-Hom-Lie algebras induced by n-Hom-Lie algebras
- Generalization of Hermite–Hadamard type inequalities for n-times differentiable functions through preinvexity
- Nonlinear iterative algorithms for quasi contraction mapping in modular space
- n-dimensional quintic and sextic functional equations and their stabilities in Felbin type spaces
- Some remarks on quasi-Frobenius rings
