A Radical Approach to Lebesgue's Theory of Integration (Mathematical Association of America Textbooks)

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9780521884747: A Radical Approach to Lebesgue's Theory of Integration (Mathematical Association of America Textbooks)
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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.

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Meant for advanced undergraduate and graduate students in mathematics, this introduction to measure theory and Lebesgue integration is motivated by the historical questions that led to its development. The author tells the story of the mathematicians who wrestled with the difficulties inherent in the Riemann integral, leading to the work of Jordan, Borel, and Lebesgue.

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"Bressoud is an insightful writer, and he presents this material in an enchanting fashion. The writing is scholarly but inviting, rigorous but readable. There are heaps of exercises, and they are quite accessible. I know of no other source with such a wealth of information about the genesis of the modern integral concept. This book will be valuable for mathematicians, for scholars of mathematical history, and certainly for students."
Steven G. Krantz, American Institute of Mathematics for The UMAP Journal

"A new and noteworthy title from Cambridge University Press! An outstanding book meant to advance undergraduate and beginning graduate students in mathematics."
B. Crstici, Mathematical Reviews

"I find it difficult to think of a better introduction to this corner store of modern mathematics and highly recommend the book to a very broad readership of students and researchers alike."
Paul Embrechts, ETH Zurich for the Journal of the American Statistical Association

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9780521711838: A Radical Approach to Lebesgue's Theory of Integration (Mathematical Association of America Textbooks)

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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2008. Hardback. Condition: New. Language: English. Brand new Book. 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. Seller Inventory # APC9780521884747

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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2008. Hardback. Condition: New. Language: English. Brand new Book. 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. Seller Inventory # APC9780521884747

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