A Primer of Lebesgue Integration

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Academic Press, Oct 16, 2001 - Mathematics - 164 pages
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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.
 

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Contents

Chapter 1 The RiemannDarboux Integral
1
Chapter 2 The Riemann Integral as a Limit of Sums
9
Chapter 3 Lebesgue Measure on 0 1
21
The Carathéodory Characterization
27
Chapter 5 The Lebesgue Integral for Bounded Functions
43
Chapter 6 Properties of the Integral
53
Chapter 7 The Integral of Unbounded Functions
61
Chapter 8 Differentiation and Integration
73
Chapter 10 The Relationship between µ and lemda
93
Chapter 11 General Measures
107
Chapter 12 Integration for General Measures
117
The RadonNikodym Theorem
127
Chapter 14 Product Measures
135
Chapter 15 The Space L2
149
Index
161
Copyright

Chapter 9 Plane Measure
85

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About the author (2001)

H.S. Bear is a professor at the University of Hawaii, Manoa and a member of both the American Mathematical Society and the Mathematical Association of America.

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