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A Measure Theoretical Version of the Aleksandrov Theorem
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Majid Gazor
Published/Copyright:
March 10, 2010
Abstract
In this paper a theorem analogous to the Aleksandrov theorem is presented in terms of measure theory. Furthermore, we introduce the condensation rank of Hausdorff spaces and prove that any ordinal number is associated with the condensation rank of an appropriate locally compact totally imperfect space. This space is equipped with a probability Borel measure which is outer regular, vanishes at singletons, and is also inner regular in the sense of closed sets.
Key words and phrases:: Aleksandrov Theorem; Borel derivative; Bernstein set; Borel measure; condensation rank; ordinal number
Received: 2006-12-06
Published Online: 2010-03-10
Published in Print: 2008-March
ยฉ Heldermann Verlag
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Keywords for this article
Aleksandrov Theorem;
Borel derivative;
Bernstein set;
Borel measure;
condensation rank;
ordinal number
Articles in the same Issue
- Functional Equations and ฮผ-Spherical Functions
- On the Uniqueness of Meromorphic Functions That Share Two Sets
- Convergence of the Ishikawa Iterates for Multi-Valued Mappings in Convex Metric Spaces
- The Existence of Solutions for Nonlinear Operator Equations
- A Measure Theoretical Version of the Aleksandrov Theorem
- Coincidence and Fixed Points of Contractive Type Multivalued Maps
- On the ๐ฟ1-Convergence of Modified Cosine Sums
- On the Approximation Properties of a Class of Convolution Type Nonlinear Singular Integral Operators
- A Metric Deformation to Obtain a Positive/Negative Gaussian Curvature on a Disk
- On Automorphism Groups of ฯ-Trees
- Growth and Approximation of Entire Harmonic Functions in ๐ ๐, ๐ > 3
- On Some Properties of the Dirichlet Problem at Resonance
- Grรถbner Bases for the Modules Over Noetherian Polynomial Commutative Rings
- Singular 2D Behaviors: Homologies
- Integrating Over the Inverse Image of Functions in the Besov Space
- The Fourth Order of Accuracy Decomposition Scheme for Abstract Hyperbolic Equation
- On a Generalization of Partial Isometries in Banach Spaces
- A Generalized Mandelbrot Set of Polynomials of Type ๐ธ๐ for Bicomplex Numbers
