Real analysis
著者
書誌事項
Real analysis
（Pearson modern classic）
Prentice Hall/Pearson, c2018
4th ed, updated printing
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注記
Includes bibliographical references (p. 497-498) and index
内容説明・目次
内容説明
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.
目次
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 Ρ Spaces: Completeness and Approximation
8. The L Ρ 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 Ρ Spaces: Completeness, Duality and Weak Convergence
20. The Construction of Particular Measures
21. Measure and Topology
22. Invariant Measures
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