《實分析教程（第2版）》是2013年1月1日世界圖書出版社出版的圖書，作者麥克唐納（McDonald J.N.）。
基本介紹
- 中文名：實分析教程（第2版）
- 作者：麥克唐納（McDonald J.N.）
- ISBN：9787510052637
- 頁數：667頁
- 定價：118.20元
- 出版社：世界圖書出版社
- 出版時間：2013年1月1日
內容簡介,圖書目錄,
內容簡介
《實分析教程（第2版）》是一部備受專家好評的教科書，書中用現代的方式清晰論述了實分析的概念與理論，定理證明簡明易懂，可讀性強，全書共有200道例題和1200例習題。《實分析教程（第2版）》的寫法像一部文學讀物，這在數學教科書很少見，因此閱讀《實分析教程（第2版）》會是一種享受。
圖書目錄
About the Authors Preface
PART ONE. Set Theory， Real Numbers， and Calculus
1. SET THEORY Biography： Georg Cantor
1.1 Basic Definitions and Properties
1.2 Functions and Sets
1.3 Equivalence of Sets； Countability
1.4 Algebras， a-Algebras， and Monotone Classes
2. THE REAL NUMBER SYSTEM AND CALCULUS
Biography： Georg Friedrich Bernhard Riemann
2.1 The ReaINumber System
2.2 Sequences of Real Numbers
2.3 Open and Closed Sets
2.4 Real-Valued Functions
2.5 The Cantor Set and Cantor Function
2.6 The Riemann Integral
PART TWO. Measure， Integration， and DifFerentiation
3. LEBESGUE MEASURE ON THE REAL LINE
Biography： Emile Felix-Edouard-Justrn Borel
3.1 Borel Measurable Functions and Borel Sets
3.2 Lebesgue Outer Measure
3.3 Further Properties of Lebesgue Outer Measure
3.4 Lebesgue Measure
4. THE LEBESGUE INTEGRAL ON THE REAL LINE
Biography： Henri Leon Lebesgue
4.1 The Lebesgue Integral for Nonnegative Functions
4.2 Convergence Properties of the Lebesgue Integral for Nonnegative Functions
4.3 The General Lebesgue Integral
4.4 Lebesgue Almost Everywhere
5. ELEMENTS OF MEASURE THEORY
Biography： Constantin Caratheodory
5.1 MeasureSpaces
5.2 Measurable Functions
5.3 The Abstract Lebesgue Integral for Nonnegative Functions
5.4 The General Abstract Lebesgue Integral
5.5 Convergence in Measure
6 .EXTENSIONS TO MEASURES AND PRODUCT MEASURE
Biography： Guido Fubini
6.1 Extensions to Measures
6.2 The Lebesgue-Stieltjes Integral
6.3 Product Measure Spaces
6.4 Iteration oflntegrals in Product Measure Spaces
7. ELEMENTS OF PROBABILITY
Biography： Andrei Niko/aewch Kolmogorov
7.1 The Mathematical Model for Probability
7.2 Random Variables
7.3 Expectation of Random Variables
7.4 The Law of Large Numbers
