Articles liés à A Radical Approach to Lebesgue's Theory of Integration

A Radical Approach to Lebesgue's Theory of Integration - Couverture souple

Bressoud, David M.

 
9780521711838: A Radical Approach to Lebesgue's Theory of Integration
Couverture souple
ISBN 10 : 0521711835 ISBN 13 : 9780521711838
Editeur : Cambridge University Press, 2008

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Revue de presse

'This introduction to measure theory and Lebesgue integration is intended for advancerd undergraduate and graduate students in mathematics, and is rooted in and motivated by the historical questions that led to its development.' The Times Higher Education Supplement

'Bressoud is an insightful writer and he presents this material in an enchanting fashion. The writing is scholarly but inviting, rigourous but readable.' The UMAP Journal

'The way that facts are presented makes the book accessible for graduate or advanced undergraduate students as an alternative to the standard approach of teaching real analysis. The book will be interesting for teachers as well.' EMS Newsletter

'I find it difficult to think of a better introduction to this cornerstone of modern mathematics and highly recommend the book to a very broad readership of students and researchers alike.' Journal of the American Statistical Association

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
2008
Langue
anglais
ISBN 10 
0521711835
ISBN 13 
9780521711838
Reliure
Broché
Numéro d'édition
1
Nombre de pages
344
Coordonnées du fabricant
non disponible
Personne responsable
Avery
https://www.avery.fr/

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Dardilly
France