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On the Uniqueness of Lebesgue and Borel Measures
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A. B. Kharazishvili
Published/Copyright:
June 4, 2010
Abstract
We consider the uniqueness property for various invariant measures. Primarily, we discuss this property for the standard Lebesgue measure on the n–dimensional Euclidean space Rn (sphere Sn) and for the standard Borel measure on the same space (sphere), which is the restriction of the Lebesgue measure to the Borel σ–algebra of Rn (Sn). The main goal of the paper is to show an application of the well known theorems of Ulam and Ershov to the uniqueness property of Lebesgue and Borel measures.
Key words and phrases.: Invariant measure; quasiinvariant measure; uniqueness property; real–valued measurable cardinal; measure extension theorem
Received: 1996-11-15
Revised: 1997-03-05
Published Online: 2010-06-04
Published in Print: 1997-June
©Heldermann Verlag
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Keywords for this article
Invariant measure;
quasiinvariant measure;
uniqueness property;
real–valued measurable cardinal;
measure extension theorem
Articles in the same Issue
- Optimal Synthesis for Nonoscillatory Controlled Objects
- Forced Oscillations of First Order Nonlinear Neutral Differential Equations
- Continuity of the Superposition of Set–Valued Functions
- On the Uniqueness of Lebesgue and Borel Measures
- Optimality Conditions for Control Problems Governed by Abstract Semilinear Differential Equations in Complex Banach Spaces
- On the Continuity of Random Operators
- Norms on Possibilities II: More CCC Ideals on 2ω
- Stationary Solutions for Heat Equation Perturbed by General Additive Noise
- Note on Decreasing Rearrangement of Fourier Series
