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A Radical Approach to Lebesgues's Theory of Integration (Softcover)
"Meant for advanced undergraduate and graduate students in mathematics, this lively introduction to measure theory and Lebesgue integration is rooted in and motivated by the historical questions that led to its development. The author stresses the original purpose of the definitions and theorems and highlights some of the difficulties that were encountered as these ideas were refined." — From the back cover
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VERY GOOD: This book is in very good condition, showing only slight signs of use and wear.
This book belongs to the MAA Textbooks series from Cambridge University Press, published on behalf of the Mathematical Association of America.
Continued from the back cover: “The story begins with Riemann’s definition of the integral, a definition created so that he could understand how broadly one could define a function and yet have it be integrable. The reader then follows the efforts of many mathematicians who wrestled with the difficulties inherent in the Riemann integral, leading to the work in the late nineteenth and early twentieth centuries of Jordan, Borel, and Lebesgue, who finally broke with Riemann’s definition. Ushering in a new way of understanding integration, they opened the door to fresh and productive approaches to many of the previously intractable problems of analysis.”
- The Riemann Integral
- Explorations of R
- Nowhere Dense Sets and the Problem with the Fundamental Theorem of Calculus
- The Development of Measure Theory
- The Lebesgue Integral
- The Fundamental Theorem of Calculus
- Fourier Series
- Other Directions
- Hints to Selected Exercises
The textbook ends with Bibliography and Index.
- Bressoud, David M.
- Cambridge University Press
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