A Primer of Lebesgue Integration
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Table of contents
- A Primer of Lebesgue Integrationi
- Copyright Pageii
- Contentsv
- Preface to the First Editionvii
- Preface to the Second Editionxi
- Chapter 1. The Riemann–Darboux Integral1
- Chapter 2. The Riemann Integral as a Limit of Sums9
- Chapter 3. Lebesgue Measure on (0, 1)21
- Chapter 4. Measurable Sets: The Carathéodory Characterization27
- Chapter 5. The Lebesgue Integral for Bounded Functions43
- Chapter 6. Properties of the Integral53
- Chapter 7. The Integral of Unbounded Functions61
- Chapter 8. Differentiation and Integration73
- Chapter 9. Plane Measure85
- Chapter 10. The Relationship between µ and lemda93
- Chapter 11. General Measures107
- Chapter 12. Integration for General Measures117
- Chapter 13. More Integration: The Radon–Nikodym Theorem127
- Chapter 14. Product Measures135
- Chapter 15. The Space L2149
- Index161
The Lebesgue integral is now standard for both applications and advanced mathematics. This books starts with a review of the familiar calculus integral and then constructs the Lebesgue integral from the ground up using the same ideas. A Primer of Lebesgue Integration has been used successfully both in the classroom and for individual study.
Bear presents a clear and simple introduction for those intent on further study in higher mathematics. Additionally, this book serves as a refresher providing new insight for those in the field. The author writes with an engaging, commonsense style that appeals to readers at all levels.
Bear presents a clear and simple introduction for those intent on further study in higher mathematics. Additionally, this book serves as a refresher providing new insight for those in the field. The author writes with an engaging, commonsense style that appeals to readers at all levels.