Author: Alan J. Weir
Publisher: Cambridge University Press
Keywords: measure, integration, lebesgue
Number of Pages: 296
Published: 1973-06-29
List price: $53.00
ISBN-10: 0521097517
ISBN-13: 9780521097512

Lebesgue integration is a technique of great power and elegance which can be applied in situations where other methods of integration fail. It is now one of the standard tools of modern mathematics, and forms part of many undergraduate courses in pure mathematics. Dr Weir’s book is aimed at the student who is meeting the Lebesgue integral for the first time. Defining the integral in terms of step functions provides an immediate link to elementary integration theory as taught in calculus courses. The more abstract concept of Lebesgue measure, which generalises the primitive notions of len

Author: William Dunham
Publisher: Princeton University Press
Keywords: lebesgue, newton, masterpieces, gallery, calculus
Number of Pages: 256
Published: 2008-07-01
List price: $19.95
ISBN-10: 0691136262
ISBN-13: 9780691136264

More than three centuries after its creation, calculus remains a dazzling intellectual achievement and the gateway into higher mathematics. This book charts its growth and development by sampling from the work of some of its foremost practitioners, beginning with Isaac Newton and Gottfried Wilhelm Leibniz in the late seventeenth century and continuing to Henri Lebesgue at the dawn of the twentieth--mathematicians whose achievements are comparable to those of Bach in music or Shakespeare in literature. William Dunham lucidly presents the definitions, theorems, and proofs. "Students of literatur

Author: Russell A. Gordon
Publisher: American Mathematical Society
Keywords: graduate, studies, mathematics, henstock, perron, lebesgue, denjoy, integrals
Number of Pages: 395
Published: 1994-08-01
List price: $50.00
ISBN-10: 0821838059
ISBN-13: 9780821838051

This book provides an elementary, self-contained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. The Lebesgue integral and its essential properties are first developed in detail. The other three integrals are all generalizations of the Lebesgue integral that satisfy the ideal version of the Fundamental Theorem of Calculus: if $F$ is differentiable on the interval $[a,b]$, then $F’$ is integrable on $[a,b]$ and $int _a^b F’= F(b) - F(a)$. One of the book’s unique features is that the Denjoy, Perron, and Henstock integrals are each

Author: Thomas Hawkins
Publisher: Amer Mathematical Society
Keywords: chelsea, publishing, series, ams, development, theory, integration, origins, lebesgue
Number of Pages: 227
Published: 2001-09
List price: $35.00
ISBN-10: 0821829637
ISBN-13: 9780821829639

In this book, Hawkins elegantly places Lebesgue’s early work on integration theory within in proper historical context by relating it to the developments during the nineteenth century that motivated it and gave it significance and also to the contributions made in this field by Lebesgue’s contemporaries. Hawkins was awarded the 1997 MAA Chauvenet Prize and the 2001 AMS Albert Leon Whiteman Memorial Prize for notable exposition and exceptional scholarship in the history of mathematics.

Author: David M. Bressoud
Publisher: Cambridge University Press
Keywords: association, america, textbooks, mathematical, integration, approach, lebesgue, theory, radical
Number of Pages: 344
Published: 2008-01-14
List price: $39.99
ISBN-10: 0521711835
ISBN-13: 9780521711838

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

Author: Frank Burk
Publisher: Wiley-Interscience
Keywords: series, texts, monographs, tracts, wiley, mathematics, measure, integration, introduction, applied, lebesgue
Number of Pages: 312
Published: 1997-11-03
List price: $177.00
ISBN-10: 0471179787
ISBN-13: 9780471179788

A superb text on the fundamentals of Lebesgue measure and integration.This book is designed to give the reader a solid understanding of Lebesgue measure and integration. It focuses on only the most fundamental concepts, namely Lebesgue measure for R and Lebesgue integration for extended real-valued functions on R. Starting with a thorough presentation of the preliminary concepts of undergraduate analysis, this book covers all the important topics, including measure theory, measurable functions, and integration. It offers an abundance of support materials, including helpful illustrations, examp

Authors:Douglas S Kurtz, Charles W. Swartz,
Publisher: World Scientific Publishing Company
Keywords: mcshane, series, real, analysis, kurzweil, henstock, integration, integrals, riemann, lebesgue, theories
Number of Pages: 268
Published: 2004-09
List price: $73.00
ISBN-10: 9812388435
ISBN-13: 9789812388438

This book presents a historical development of the integration theories of Riemann, Lebesgue, Henstock-Kurzweil, and McShane, showing how new theories of integration were developed to solve problems that earlier theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. The chapters covering each integral are essentially independent and can be used separately in teaching a portion of an introductory course on real analysis. There is a sufficient supply of exercises to make the book useful as a textbook.