Nonstandard Analysis and Vector Lattices

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.- 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.- § 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.