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.
Advanced undergraduate and beginning graduate students in mathematics.
The Riemann-Darboux Integral; The Riemann Integral as a Limit of Sums; Lebesgue Measure on (0, 1); Measurable Sets: The Caratheodory Characterization; The Lebesgue Integral for Bounded Functions; Properties of the Integral; The Integral of Unbounded Functions; Differentiation and Integration; Plane Measure; The Relationship between µ and General Measures; Integration for General Measures; More Integration: The Radon-Nikodym Theorem; Product Measures; The Space L2; Index
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- © Academic Press 2002
- 17th September 2001
- Academic Press
- eBook ISBN:
- Hardcover ISBN:
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.
University of Hawaii at Manoa, Honolulu, U.S.A.
"This well-written little book provides ... an introduction to the Lebesgue integral. The book is written very clearly and suggestively and can be recommended to students." Zentralblatt for Mathematik