《實分析》是2019年世界圖書出版公司出版的圖書，作者是G.B.弗蘭德。
基本介紹
- 中文名：實分析
- 作者：G.B.弗蘭德
- 出版時間：2019年5月
- 出版社：世界圖書出版公司
- ISBN：9787519260729
- 定價：89 元
- 開本：16 開
- 裝幀：平裝-膠訂
內容簡介,圖書目錄,作者簡介,
內容簡介
本書是Folland教授的名著《實分析》的第二版。與*版相比，在一些內容的編排上作了適當調整，同時引入了一些新的內容，去掉了已經過時的內容，更有利於學生學習與思考。作為一部優秀的教材，內容不僅涵蓋了分析學的基本內容和技巧，還介紹了一些從事其他領域的研究工作所必需的基礎知識。此外，教材中的大量習題，能夠進一步拓展思維，從而易於更加深入地了解這些內容背後的真實想法。本書適用於理工類專業及相關專業的研究生。
圖書目錄
Preface
0 Prologue
0.1 The Language of Set Theory
0.2 Orderings
0.3 Cardinality
0.4 More about Well Ordered Sets
0.5 The Extended Real Number System
0.6 Metric Spaces
0.7 Notes and References
1 Measures
1.1 Introduction
1.2 a-algebras
1.3 Measures
1.4 Outer Measures
1.5 Borel Measures on the Real Line
1.6 Notes and References
2 Integration
2.1 Measurable Functions
2.2 Integration of Nonnegative Functions
2.3 Integration of Complex Functions
2.4 Modes of Convergence
2.5 Product Measures
2.6 The n-dimensional Lebesgue Integral
2.7 Integration in Polar Coordinates
2.8 Notes and References
3 Signed Measures and Differentiation
3.1 Signed Measures
3.2 The Lebesgue-Radon-Nikodym Theorem
3.3 Complex Measures
3.4 Differentiation on Euclidean Space
3.5 Functions of Bounded Variation
3.6 Notes and References
4 Point Set Topology
4.1 Topological Spaces
4.2 Continuous Maps
4.3 Nets
4.4 Compact Spaces
4.5 Locally Compact Hausdorff Spaces
4.6 Two Compactness Theorems
4.7 The Stone-Weierstrass Theorem
4.8 Embeddings in Cubes
4.9 Notes and References
5 Elements of Functional Analysis
5.1 Normed Vector Spaces
5.2 Linear Functionals
5.3 The Baire Category Theorem and its Consequences
5.4 Topological Vector Spaces
5.5 Hilbert Spaces
5.6 Notes and References
6 LP Spaces
6.1 Basic Theory of LP Spaces
6.2 The Dual of LP
6.3 Some Useful Inequalities
6.4 Distribution Functions and Weak LP
6.5 Interpolation of LP Spaces
6.6 Notes and References
7 Radon Measures
7.1 Positive Linear Functionats on Cc(X)
7.2 Regularity and Approximation Theorems
7.3 The Dual of Co(X)
7.4 Products of Radon Measures
7.5 Notes and References
8 EIements of Fourier Analysis
8.1 Preliminaries
8.2 Convolutions
8.3 The Fourier Transform
8.4 Summation of Fourier Integrals and Series
8.5 Pointwise Convergence of Fourier Series
8.6 Fourier Analysis of Measures
8. 7 Applications to Partial Differential Equations
8.8 Notes and References
9 Elements of Distribution Theory
9.1 Distributions
9.2 Compactly Supported, Tempered, and Periodic
Distributions
9.3 Sobolev Spaces
9.4 Notes and References
10 Topics in Probability Theory
10.1 Basic Concepts
10.2 The Law of Large Numbers
10.3 The Central Limit Theorem
10.4 Construction of Sample Spaces
10.5 The Wiener Process
10.6 Notes and References
11 More Measures and Integrals
11.1 Topological Groups and Haar Measure
11.2 Hausdorff Measure
11.3 Self-similarity and Hausdorff Dimension
11.4 Integration on Manifolds
11.5 Notes and References
Bibliography
Index of Notation
Index
作者簡介
Gerald B. Folland，1953年於美國普林斯頓大學獲得數學博士學位，美國華盛頓大學西雅圖分校數學系教授。早年師從分析大師E.M.Stein學習，在調和分析、複分析、微分方程等領域都有著傑出的工作。他的著作《相空間中的分析》、《抽象調和分析》、《實分析》等一直是國內外數學專業以及相關專業研究生的重要參考書籍。
