| 词条 | 实分析原理 |
| 释义 | 图书信息出版社: 世界图书出版公司; 第3版 (2009年1月1日) 外文书名: Principles of Real Analysis 平装: 415页 正文语种: 英语 开本: 24 ISBN: 9787506292726 条形码: 9787506292726 尺寸: 22.2 x 14.8 x 2.2 cm 重量: 522 g 作者简介作者：(美国)阿里普兰蒂斯 (Charalambos D.Aliprantis) (美国)Owen burkinshaw 内容简介《实分析原理(第3版)》主要内容：This is the third edition of Principles of Real Alysis, first published in 1981. The aim of this edition is to accommodate the current needs for the traditional real analysis course that is usually taken by the senior undergraduate or by the first year graduate student in mathematics. This edition differs substantially from the second edition. Each chapter has been greatly improved by incorporating new material and by rearranging the old material. Moreover, a new chapter （Chapter 6） on Hilbert spaces and Fourier analysis has been added. 目录Preface CHAPTER 1. FUNDAMENTALS OF REAL ANALYSIS 1. Elementary Set Theory 2. Countable and Uncountable Sets 3. The Real Numbers 4. Sequences of Real Numbers 5. The Extended Real Numbers 6. Metric Spaces 7. Compactness in Metric Spaces CHAPTER 2. TOPOLOGY AND CONTINUITY 8. Topological Spaces 9. Continuous Real-Valued Functions 10. Separation Properties of Continuous Functions 11. The Stone-Weierstrass Approximation Theorem CHAPTER 3. THE THEORY OF MEASURE 12. Semirings and Algebras of Sets 13. Measures on Semirings 14. Outer Measures and Measurable Sets 15. The Outer Measure Generated by a Measure 16. Measurable Functions 17. Simple and Step Functions 18. The Lebesgue Measure 19. Convergence in Measure 20. Abstract Measurability CHAPTER 4. THE LEBESGUE INTEGRAL 21. Upper Functions 22. Integrable Functions 23. The Riemann Integral as a Lebesgue Integral 24. Applications of the Lebesgue Integral 25. Approximating Integrable Functions 26. Product Measures and Iterated Integrals CHAPTER 5. NORMED SPACES AND Lp-SPACES 27. Normed Spaces and Banach Spaces 28. Operators Between Banach Spaces 29. Linear Functionals 30. Banach Lattices 31. Lp-Spaces CHAPTER 6. HILBERT SPACES 32. Inner Product Spaces 33. Hilbert Spaces 34. Orthonormal Bases 35. Fourier Analysis CHAPTER 7. SPECIAL TOPICS IN INTEGRATION 36. Signed Measures 37. Comparing Measures and the Radon-Nikodym Theorem 38. The Riesz Representation Theorem 39. Differentiation and Integration 40. The Change of Variables Formula Bibliography List of Symbols Index |
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