Nonstandard Analysis and Vector Lattices
Nonstandard methods of analysis consist generally in comparative study of two interpretations of a mathematical claim or construction given as a formal symbolic expression by means of two different set-theoretic models: one, a "standard" model and the other, a "nonstandard" model...
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| Format: | eBook |
| Language: | English |
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Dordrecht
Springer Netherlands
2000, 2000
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| Edition: | 1st ed. 2000 |
| Series: | Mathematics and Its Applications
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 3. Dual Banach Bundles
- § 3.1. Auxiliary Results
- § 3.2. Homomorphisms of Banach Bundles
- § 3.3. An Operator Bundle
- § 3.4. The Dual of a Banach Bundle
- § 3.5. Weakly Continuous Sections
- References
- 4. Infinitesimals in Vector Lattices
- § 4.0. Preliminaries
- § 4.1. Saturated Sets of Indivisibles
- § 4.2. Representation of Archimedean Vector Lattices
- § 4.3. Order, Relative Uniform Convergence, and the Archimedes Principle
- § 4.4. Conditional Completion and Atomicity
- § 4.5. Normed Vector Lattices
- § 4.6. Linear Operators Between Vector Lattices
- § 4.7. *-Invariant Homomorphisms
- § 4.8. Order Hulls of Vector Lattices
- § 4.9. Regular Hulls of Vector Lattices
- § 4.10. Order and Regular Hulls of Lattice Normed Spaces
- § 4.11. Associated Banach—Kantorovich Spaces
- References
- 5. Vector Measures andDominated Mappings
- § 5.1. Vector Measures
- § 5.2. Quasi-Radon and Quasiregular Measures
- 1. Nonstandard Methods and Kantorovich Spaces
- § 1.1. Zermelo—Fraenkel Set Theory
- § 1.2. Boolean Valued Set Theory
- § 1.3. Internal and External Set Theories
- § 1.4. Relative Internal Set Theory
- § 1.5. Kantorovich Spaces
- § 1.6. Reals Inside Boolean Valued Models
- § 1.7. Functional Calculus in Kantorovich Spaces
- § 1.8. Lattice Normed Spaces
- § 1.9. Nonstandard Hulls
- § 1.10. The Loeb Measure
- § 1.11. Boolean Valued Modeling in a Nonstandard Universe
- § 1.12. Infinitesimal Modeling in a Boolean Valued Universe
- § 1.13. Extension and Decomposition of Positive Operators
- § 1.14. Fragments of Positive Operators
- § 1.15. Order Continuous Operators
- § 1.16. Cyclically Compact Operators
- References
- 2. Functional Representation of a Boolean Valued Universe
- § 2.1. Preliminaries
- § 2.2. The Concept of Continuous Bundle
- § 2.3. A Continuous Polyverse
- § 2.4. Functional Representation
- References
- § 5.3. Integral Representations and Extension of Measures
- § 5.4. The Fubini Theorem
- § 5.5. The Hausdorff Moment Problem
- § 5.6. The Hamburger Moment Problem
- § 5.7. The Hamburger Moment Problem for Dominant Moment Sequences
- § 5.8. Dominated Mappings
- § 5.9. The Bochner Theorem for Dominated Mappings
- § 5.10. Convolution
- § 5.11. Boolean Valued Interpretation of the Wiener Lemma
- References
- Notation Index