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The Algebraic Sum of Two Absolutely Negligible Sets Can be an Absolutely Nonmeasurable Set
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Alexander Kharazishvili
Published/Copyright:
September 1, 2005
Abstract
We prove that there exist two absolutely negligible subsets A and B of the real line R, whose algebraic sum AB is an absolutely nonmeasurable subset of R. We also obtain some generalization of this result and formulate a relative open problem for uncountable commutative groups.
Key words and phrases:: Invariant measure; quasi-invariant measure; absolutely negligible set; absolutely nonmeasurable set; extension of measure
Received: 2004-05-24
Published Online: 2005-September
Published in Print: 2005-September
Heldermann Verlag
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Keywords for this article
Invariant measure;
quasi-invariant measure;
absolutely negligible set;
absolutely nonmeasurable set;
extension of measure
Articles in the same Issue
- Interval Oscillation Criteria of Matrix Differential Systems with Damping
- On a Normal of the Distribution of Hyperplane Elements in an Affine Space
- Admissible Diagrams for 𝐺(𝑚, 1, 𝑛)
- Monotonicity and the Asymptotic Estimate of Bleimann Butzer and Hahn Operators Based on Q-Integers
- On Weakly Primary Ideals
- Hardy's Inequality in a Variable Exponent Sobolev Space
- Deciding Linear Disjointness of Finitely Generated Differential Fields
- The Algebraic Sum of Two Absolutely Negligible Sets Can be an Absolutely Nonmeasurable Set
- On Linear Conjugation Problems with a Doubly Periodic Jump Line (The Case Of Open Arcs)
- On the Uniqueness Property for Invariant Measures
- Beyond Moser's Conjecture on Grunsky Inequalities
- Set-Theoretic Properties of Schmidt's Ideal
- Composition Operators on 𝑄𝑝 Spaces
- On 𝑚𝑠𝑘-Images of Metric Spaces
- On Nonnegative Solutions of Initial Value Problems for Second Order Linear Functional Differential Equations
- A Note on Fourier Coefficients of Functions of Generalized Wiener Class
- Periodic Solutions of Higher Order Nonlinear Difference Equations Via a Continuation Theorem
- On a Singular Direction of a Meromorphic Function
- Extension of Multiresolution Analysis and the Construction of Orthogonal Multiwavelets
- On YJ-Injectivity and Annihilators
