目錄
Chapter 1 Sets
1.1 Sets and Their Operations
1.2 Mapping and Cardinality
1.3 One Dimensional Open Sets,Closed Sets and Their Properties
1.4 Construction of Open Sets
1.5 Distance
Exercise One
Chapter 2 Lebesgue Measure
2.1 Measure of Bounded Open and Closed Sets,and Their Properties
2.2 Measurable Set and Its Properties
2.3 The Measure of Unbounded Sets on R
Exercise Two
Chapter 3 Lebesgue Measurable Function
3.1 Lebesgue Measurable Function and Its Basic Properties
3.2 The Convergence of Measurable Function Sequence
3.3 The Construction of Measurable Functions
Exercise Three
Chapter 4 Lebesgue Integration
4.1 Introduction of Lebesgue Integration
4.2 Properties of Integration
4.3 Limit of Integral Sequences
4.4 Comparison of Riemann Integration and Lebesgue Integration
4.5 Double L-Integral and Fubini Theorem
Exercise Four
Chapter 5 Differentiation and Indefinite Integration
5.1 Differentiation of Monotonic Functions
5.2 Finite Variation Functions and Absolutely Continuous Functions
Exercise Five
Chapter 6 Lp (p?1) Space
6.1 Concepts of Lp (p?1) Space
6.2 Convergence of Lp Space
6.3 L2 (E) Space
Exercise Six
Chapter 7 The Measure of General Sets
7.1 The Measure of Ring
7.2 The Outer Measure on σ-Ring, Measurable Sets, and Extension of Measure
7.3 Generalized Measure
7.4 Product Measure and Finini Theorem
7.5 Lebesgue-Stieltjes Integration Concept
Appendix Some Math Expressions and Pronunciations
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