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A RADICAL APPROACH TO LEBESGUE'S THEORY OF INTEGRATION

A RADICAL APPROACH TO LEBESGUE'S THEORY OF INTEGRATION

A RADICAL APPROACH TO LEBESGUE'S THEORY OF INTEGRATION

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RADL
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A Radical Approach to Lebesgue's Theory of Integration by David Bressoud

This book is an introduction to measure theory and Legesgue integration rooted in and motivated by the historical questions that led to its development. It stresses the original purpose of the definitions and theorems, and highlights some of the difficulties that were encountered as these ideas were refined. The text 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 story then follows the efforts of many different mathematicians who wrestled with the difficulties inherent in the Riemann integral, leading to the work of the late 19th and early 20th centuries of Jordan, Borel and Legesgue who finally broke with Riemann's definition. This book is not intended to be read as a history of the development of analysis. Rather, it is a textbook informed by history, attempting to communicate the motivations, uncertainties, and difficulties surrounding the key concepts.

  • Brand name: MAA
  • Author: David Bressoud
  • ISBN:9780521711838
  • 320 pp.
  • Paperback
  • 2008
  • Series: Textbooks
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