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✦   LIBER   ✦

Lebesgue Integration and Measure

✍ Scribed by Alan J. Weir

Book ID
127449604
Publisher
Cambridge University Press
Year
1973
Tongue
English
Weight
6 MB
Category
Library
ISBN-13
9780521097512

No coin nor oath required. For personal study only.

✦ Synopsis

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 length, area and volume, is deduced later.The explanations are simple and detailed with particular stress on motivation. Over 250 exercises accompany the text and are grouped at the ends of the sections to which they relate: notes on the solutions are given.

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This textbook and treatise begins with classical real variables, develops the Lebesgue theory abstractly and for Euclidean space, and analyzes the structure of measures. The authors' vision of modern real analysis is seen in their fascinating historical commentary and perspectives with other fields.