出版社：世界图书出版公司北京公司
年代：2009
定价：45.0
本书曾作为美国几所大学研究生的实变函数论课程教材，使用多年。作者用代数、点集拓扑、泛函分析、测度论等现代分析手段论述实变函数论，同时也讨论一些应用问题，如厄米特函数，傅氏级数，傅氏积分，Plancherel定理，点态可求和性，大数强定理，线上的复值测度等。
Chapter One： Set Theory and Algebra
Section 1. The algebra of sets
Section 2. Relations and functions
Section 3. The axiom of choice and ordinal numbers
Section 4. Cardinal numbers and ordinal numbers
Section 5. Construction of the real and complex number fields
Chapter Two： Topology and Continuous Functions
Section 8. The riemann-Stieltjes integral
Section 9. Extending certain functionals
Section 10. Measures and measurable sets
Section 11. Measurable functions
Section 12. The abstract Lebesgue integral
Chapter Four： Function Spaces and Banach Spaces
Section 13. The spaces
Section 14. Abstract Banach spaces
Section 15. The conjugate space
Section 16. Abstract Hilbert spaces
Chapter Five： Differentiation
Section 17. Differentiable and nondifferentiable functions
Section 18. Absolutely continuous functions
Section 19. Complex measures and the LEBESGUE-RADON-NIKODYM theorem
Section 20. Applications of the LEBESGUE-RADON-NIKODYM theorem
Chapter Six： Integration on Product Spaces
Section 21. The product of two measure spaces
Section 22. Products of infinitely many measure spaces
Index of Symbols
Index of Authors and Terms
This book is first of all designed as a text for the course usually called "theory of functions of a real variable". This course is at present customarily offered as a first or second year graduate course in United States universities， although there are signs that this sort of analysis will soon penetrate upper division undergraduate curricula. We have included every topic that we think essential for the training of analysts， and we have also gone down a number of interesting bypaths. We hope too that the book will be useful as a reference for mature mathematicians and other scientific workers. Hence we have presented very general and complete versions of a number of important theorems and constructions. Since these sophisticated versions may be difficult for the beginner， we ave given elementary avatars of all important theorems， with appropriate suggestions for skipping. We have given complete definitions， explanations， and proofs throughout， so that the book should be usable for individual study as well as for a course text
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| 书名 | 实分析和抽象分析站内查询相似图书 | ||
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| 出版地 | 北京 | 出版单位 | 世界图书出版公司北京公司 |
| 版次 | 1版 | 印次 | 1 |
| 定价(元) | 45.0 | 语种 | 英文 |
| 尺寸 | 14 | 装帧 | 平装 |
| 页数 | 印数 | 1000 | |
实分析和抽象分析是世界图书出版公司北京公司于2009.04出版的中图分类号为 O17 的主题关于 实分析－研究生－教材－英文 ,数学分析－研究生－教材－英文 的书籍。