# Basic Analysis IV: Measure Theory and Integration

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- eBook:Basic Analysis IV: Measure Theory and Integration
- Author:James K. Peterson
- Edition:1 edition
- Categories:
- Data:August 13, 2020
- ISBN:1138055115
- ISBN-13:9781138055117
- Language:English
- Pages:500 pages
- Format:PDF

**Book Description**

*Basic Analysis IV:***introduces students to concepts from measure theory and continues their training in the abstract way of looking at the world. This is a most important skill to have when your life's work will involve quantitative modeling to gain insight into the real world. This text generalizes the notion of integration to a very abstract setting in a variety of ways. We generalize the notion of the length of an interval to the measure of a set and learn how to construct the usual ideas from integration using measures. We discuss carefully the many notions of convergence that measure theory provides.**

*Measure Theory and Integration***Features**

• Can be used as a traditional textbook as well as for self-study

• Suitable for advanced students in mathematics and associated disciplines

• Emphasises learning how to understand the consequences of assumptions using a variety of tools to provide the proofs of propositions

**Content**

1. Introduction

II - Classical Riemann Integration

2. An Overview of Riemann Integration

3. Bounded Variation

4. Riemann Integration

5. Further Riemann Results

III - Riemann -Stieltjes Integration

6. The Riemann -Stieltjes Integral

7. Further Riemann -Stieltjes Results

IV - Abstract Measure Theory One

8. Measurability

9. Abstract Integration

10. The Lp Spaces

V - Constructing Measures

11. Building Measures

12. Lebesgue Measure

13. Cantor Sets

14. Lebesgue -Stieltjes Measure

VI - Abstract Measure Theory Two

15. Convergence Modes

16. Decomposing Measures

17. Connections to Riemann Integration

18. Fubini Type Results

19. Differentiation

VII - Summing It All Up

20. Summing It All Up

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