A radical approach to Lebesgue's theory of integration
Author(s)
Bibliographic Information
A radical approach to Lebesgue's theory of integration
（MAA textbooks）
Cambridge University Press, 2008
- : hard
- : pbk
Available at / 20 libraries
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Science and Technology Library, Kyushu University
: hard023212007007114,
: pbk413.4/B 72031212009003272 -
Tokyo University of Agriculture and Technology Koganei Library
: hard413.460610492,
: pbk413.460607801, pbk.413.460607801, 413.460610492 -
Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science数学
: hard/B 7552080165125
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Note
Includes bibliographical references (p. 317-322) and index
Description and Table of Contents
Description
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. 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 19th and early 20th 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.
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.
by "Nielsen BookData"