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A Radical Approach to Lebesgues's Theory of Integration (Softcover)

A Radical Approach to Lebesgues's Theory of Integration (Softcover)

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VERY GOOD: This book is in very good condition, showing only slight signs of use and wear.

Product Details

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."

Chapters

  1. Introduction
  2. The Riemann Integral
  3. Explorations of R
  4. Nowhere Dense Sets and the Problem with the Fundamental Theorem of Calculus
  5. The Development of Measure Theory
  6. The Lebesgue Integral
  7. The Fundamental Theorem of Calculus
  8. Fourier Series
  9. Epilogue
Appendices
  1. Other Directions
  2. Hints to Selected Exercises
The textbook ends with Bibliography and Index.
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AUTHOR: Bressoud;David M.
PUBLISHER: Cambridge University Press
ISBN-13: 9780521711838
ISBN-10: 0521711835
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