Real Analysis (Classic Version)
Description
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. It assumes a general background in undergraduate mathematics and familiarity with the material covered in an undergraduate course on the fundamental concepts of analysis. Patrick Fitzpatrick of the University of Maryland - College Park spearheaded this revision of Halsey Royden's classic text.
This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price.
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Content
- 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 L ? Spaces: Completeness and Approximation
- 8. The L ? 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 L ? Spaces: Completeness, Duality and Weak Convergence
- 20. The Construction of Particular Measures
- 21. Measure and Topology
- 22. Invariant Measures