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This text is designed for graduate-level courses in real analysis.
Real Analysis, 4th Edition, covers the basic material that every graduate student should know in the classical theory of functions of a real variable, measure and integration theory, and some of the more important and elementary topics in general topology and normed linear space theory. This text assumes a general background in undergraduate mathematics and familiarity with the material covered in an undergraduate course on the fundamental concepts of analysis.
This text is designed for graduate-level courses in real analysis.
Real Analysis, 4th Edition, covers the basic material that every graduate student should know in the classical theory of functions of a real variable, measure and integration theory, and some of the more important and elementary topics in general topology and normed linear space theory. This text assumes a general background in undergraduate mathematics and familiarity with the material covered in an undergraduate course on the fundamental concepts of analysis.
- PART I: LEBESGUE INTEGRATION FOR FUNCTIONS OF A SINGLE REAL VARIABLE
- 1. The Real Numbers: Sets, Sequences and Functions
- 2. Lebesgue Measure
- 3. Lebesgue Measurable Functions
- 4. Lebesgue Integration
- 5. Lebesgue Integration: Further Topics
- 6. Differentiation and Integration
- 7. The LΡ Spaces: Completeness and Approximation
- 8. The LΡ Spaces: Duality and Weak Convergence
- PART II: ABSTRACT SPACES: METRIC, TOPOLOGICAL, AND HILBERT
- 9. Metric Spaces: General Properties
- 10. Metric Spaces: Three Fundamental Theorems
- 11. Topological Spaces: General Properties
- 12. Topological Spaces: Three Fundamental Theorems
- 13. Continuous Linear Operators Between Banach Spaces
- 14. Duality for Normed Linear Spaces
- 15. Compactness Regained: The Weak Topology
- 16. Continuous Linear Operators on Hilbert Spaces
- PART III: MEASURE AND INTEGRATION: GENERAL THEORY
- 17. General Measure Spaces: Their Properties and Construction
- 18. Integration Over General Measure Spaces
- 19. General LΡ Spaces: Completeness, Duality and Weak Convergence
- 20. The Construction of Particular Measures
- 21. Measure and Topology
- 22. Invariant Measures
| Erscheinungsjahr: | 2017 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: | Kartoniert / Broschiert |
| ISBN-13: | 9780134689494 |
| ISBN-10: | 0134689496 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Royden, Halsey
Fitzpatrick, Patrick |
| Hersteller: | Pearson Education (US) |
| Maße: | 233 x 176 x 29 mm |
| Von/Mit: | Halsey Royden (u. a.) |
| Erscheinungsdatum: | 21.08.2017 |
| Gewicht: | 0,874 kg |
- PART I: LEBESGUE INTEGRATION FOR FUNCTIONS OF A SINGLE REAL VARIABLE
- 1. The Real Numbers: Sets, Sequences and Functions
- 2. Lebesgue Measure
- 3. Lebesgue Measurable Functions
- 4. Lebesgue Integration
- 5. Lebesgue Integration: Further Topics
- 6. Differentiation and Integration
- 7. The LΡ Spaces: Completeness and Approximation
- 8. The LΡ Spaces: Duality and Weak Convergence
- PART II: ABSTRACT SPACES: METRIC, TOPOLOGICAL, AND HILBERT
- 9. Metric Spaces: General Properties
- 10. Metric Spaces: Three Fundamental Theorems
- 11. Topological Spaces: General Properties
- 12. Topological Spaces: Three Fundamental Theorems
- 13. Continuous Linear Operators Between Banach Spaces
- 14. Duality for Normed Linear Spaces
- 15. Compactness Regained: The Weak Topology
- 16. Continuous Linear Operators on Hilbert Spaces
- PART III: MEASURE AND INTEGRATION: GENERAL THEORY
- 17. General Measure Spaces: Their Properties and Construction
- 18. Integration Over General Measure Spaces
- 19. General LΡ Spaces: Completeness, Duality and Weak Convergence
- 20. The Construction of Particular Measures
- 21. Measure and Topology
- 22. Invariant Measures
| Erscheinungsjahr: | 2017 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: | Kartoniert / Broschiert |
| ISBN-13: | 9780134689494 |
| ISBN-10: | 0134689496 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Royden, Halsey
Fitzpatrick, Patrick |
| Hersteller: | Pearson Education (US) |
| Maße: | 233 x 176 x 29 mm |
| Von/Mit: | Halsey Royden (u. a.) |
| Erscheinungsdatum: | 21.08.2017 |
| Gewicht: | 0,874 kg |
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