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On Vector Sums of Measure Zero Sets
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A. Kharazishvili
Veröffentlicht/Copyright:
24. Februar 2010
Abstract
We consider the behaviour of measure zero subsets of a vector space under the operation of vector sum. The question whether the vector sum of such sets can be nonmeasurable is discussed in connection with the measure extension problem, and a certain generalization of the classical Sierpiński result [Fund. Math. 1: 105–111, 1920] is presented.
Key words and phrases:: Vector sum; measure zero set; transformation group; quasi-invariant measure; nonmeasurable set; absolutely negligible set
Received: 2001-03-12
Published Online: 2010-02-24
Published in Print: 2001-September
© Heldermann Verlag
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Schlagwörter für diesen Artikel
Vector sum;
measure zero set;
transformation group;
quasi-invariant measure;
nonmeasurable set;
absolutely negligible set
Artikel in diesem Heft
- A New Method of Solving the Basic Plane Boundary Value Problems of Statics of the Elastic Mixture Theory
- Euler Polynomials and the Related Quadrature Rule
- MD-Numbers and Asymptotic MD-Numbers of Operators
- Boundary Variational Inequality Approach in the Anisotropic Elasticity for the Signorini Problem
- On Vector Sums of Measure Zero Sets
- Hyper-Holomorphic Cells and Fredholm Theory
- On a Representation of the Derivative of a Conformal Mapping
- On a Trace Inequality for One-Sided Potentials and Applications to the Solvability of Nonlinear Integral Equations
- Quasiconformal Deformations of Holomorphic Functions
- Convolutional Codes and Frequency Responses
- Boundary Integral Equations of Plane Elasticity in Domains with Peaks
- Pluriregular, Plurigeneralized Regular Equations in Clifford Analysis
- On Volterra Type Singular Integral Equations
