A Radical Approach to Lebesgue's Theory of Integration / Edition 1

A Radical Approach to Lebesgue's Theory of Integration / Edition 1

by David M. Bressoud
     
 

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ISBN-10: 0521711835

ISBN-13: 9780521711838

Pub. Date: 01/31/2008

Publisher: Cambridge University Press

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

Overview

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.

Product Details

ISBN-13:
9780521711838
Publisher:
Cambridge University Press
Publication date:
01/31/2008
Series:
Mathematical Association of America Textbooks Series
Edition description:
New Edition
Pages:
344
Sales rank:
807,455
Product dimensions:
5.98(w) x 8.98(h) x 0.67(d)

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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