Lebesgue Integration and Measure

By Alan J. Weir

Book Overview

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.

• Format: Paperback
• Language: English
• ISBN: 0521097517
• ISBN13: 9780521097512
• Release Date: June 1973
• Publisher: Cambridge University Press
• Length: 296 Pages
• Weight: 0.05 lbs.
• Dimensions: 0.7" x 6.5" x 8.6"

Customer Reviews

Great book

Its a very good text for a first meeting on Lebesgue integration, measure and functional analysis. Rigorous, elegant and simple. A quality book for pure and applied mathematics.However I found two little mistakes:In page 151, in the proof of the integral of a transformation, he makes use of the Dominated Convergence Theorem two times (one first time, at the begining of page 151, is right). Thats wrong because we can't "dominate" the function "g" when K -> inf. The correct proof involves divide the function in positive and negative parts and then aplicate Monotone Convergence Theorem. The same in the end of the proof when he generalizes to infinite measure sets.<p>In page 157, equation (7) should be verified when ||h||<2*delta, not ||h||<delta as he writes. This is to assure that the set C+ is contained in that region.<p>Anyway, a brilliant text. Purchase it.

Good introduction to the theory of Lebesgue integration

I picked up this book on a trip to London. I've known some complex analysis and real analysis, and I decided to learn some Lebesgue on my own; ergo the purchase of this book. The style of writing is very lucid: quite informal at times, and the math part is really well-presented (the explanation on 'measure zero' set, for example, is clear, and mathematically rigorous). The topics chosen are not in-depth (I learnt much more on the topic during an actual course in college), but the book definitely works well as a supplement reading, when you are taking real analysis course.