A Radical Approach to Lebesque's Theory of Integration

David M. Bressoud

ISBN 10: 0521711835 / ISBN 13: 9780521711838

Published by Cambridge University Press, 2008

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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 # 9780521711838

Bibliographic Details

• Title: A Radical Approach to Lebesque's Theory of Integration
• Publisher: Cambridge University Press
• Publication Date: 2008
• Language: English
• ISBN 10: 0521711835
• ISBN 13: 9780521711838
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 254W x 178H x 19D millimeters 254 millimeters width by 178 millimeters height by 19 millimeters depth
• Weight: 648 grams

About this title

Synopsis

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.

Book Description

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.