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A Radical Approach to Lebesgue s Theory of Integration 1st Edition by David Bressoud ISBN 978-0521711838 0521711835

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A Radical Approach to Lebesgue s Theory of Integration 1st Edition David M. Bressoud Digital Instant Download

Author(s): David M. Bressoud
ISBN(s): 9780521884747, 0521884748
Edition: 1
File Details: PDF, 25.89 MB
Year: 2008
Language: english
SKU: EB-1740040 Category: Tag:

A Radical Approach to Lebesgue s Theory of Integration 1st Edition by David M. Bressoud – Ebook PDF Instant Download/Delivery:  978-0521711838, 0521711835
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Product details: 

ISBN 10:   0521711835

ISBN 13: 978-0521711838

Author: David M. Bressoud

This lively introduction to measure theory and Lebesgue integration is motivated by the historical questions that led to its development. The author stresses the original purpose of the definitions and theorems, highlighting the difficulties mathematicians encountered as these ideas were refined. The story begins with Riemann’s definition of the integral, and then follows the efforts of those who wrestled with the difficulties inherent in it, until Lebesgue finally broke with Riemann’s definition. With his new way of understanding integration, Lebesgue opened the door to fresh and productive approaches to the previously intractable problems of analysis.
 

Table of contents: 

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
  A. Other Directions
  B. Hints to Selected Exercises

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Tags: David Bressoud, A Radical Approach, Lebesgue s Theory