A Radical Approach to Lebesgue's Theory of Integration
By (author) David M. Bressoud
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Radical Approach to Lebesgue's Theory of Integration by David M. Bressoud
Book DescriptionMeant 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.
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Book DetailsISBN: 9780521711838
(228mm x 152mm x 18mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 14-Jan-2008
Country of Publication: United Kingdom
Books By Author David M. Bressoud
Radical Approach to Lebesgue's Theory of Integration, Hardback (January 2008)
An introduction to measure theory and Lebesgue integration rooted in the historical questions that led to its development.
Proofs and Confirmations, Paperback (August 1999)» View all books by David M. Bressoud
An introduction to recent developments in algebraic combinatorics and an illustration of how research in mathematics actually progresses.
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