Real analysis
著者
書誌事項
Real analysis
Prentice-Hall, c1997
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注記
Includes index
内容説明・目次
内容説明
For beginning graduate-level courses in Real Analysis, Measure Theory, Lebesque Integration, and Functional Analysis.
An important new graduate text that motivates the reader by providing the historical evolution of modern analysis. Sensitive to the needs of students with varied backgrounds and objectives, this text presents the tools, methods and history of analysis. The text includes the topics that "every graduate student must know" as well as specialized topics that prepare students for further study in analysis. User-friendly in approach, it includes numerous examples and exercises to illustrate and motivate the concepts.
目次
1. Background and Preview.
2. Measure Spaces.
3. Metric Outer Measures.
4. Measurable Functions.
5. Integration.
6. Fubini's Theorem.
7. Differentiation.
8. Differentiation of Measures.
9. Metric Spaces.
10. Baire Category.
11. Analytic Sets.
12. Banach Spaces.
13. The Lp Spaces
14. Hilbert Spaces.
15. Fourier Series.
Index.
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