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內容簡介

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

目錄

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

前言/序言

實分析和抽象分析 下載 mobi epub pdf txt 電子書

評分☆☆☆☆☆

經典，內容專業

評分☆☆☆☆☆

gtm25；比較老瞭。

評分☆☆☆☆☆

非常好的分析教程，也可以做工具書來查

評分☆☆☆☆☆

gtm25；比較老瞭。

評分☆☆☆☆☆

joli

評分☆☆☆☆☆

GTM係列，自然經典！本書在分析方麵還是不錯的

評分☆☆☆☆☆

該書內容詳盡，敘述清晰，很不錯的書！

評分☆☆☆☆☆

好～！

評分☆☆☆☆☆

雖然齣版瞭很多年瞭，這本書依然經典。過去有人曾經翻譯瞭這本書，但是還是原版最好。

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