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【转贴】A Primer of Lebesgue Integration, Second Edition
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A Primer of Lebesgue Integration, Second Edition Publisher: Academic Press Number Of Pages: 175 Publication Date: 2001-09-17 Sales Rank: 774793 ISBN / ASIN: 0120839717 EAN: 9780120839711 Binding: Hardcover Manufacturer: Academic Press Studio: Academic Press Average Rating: 5 The Lebesgue integral is now standard for both applications and advanced mathematics. This books starts with a review of the familiar calculus integral and then constructs the Lebesgue integral from the ground up using the same ideas. A Primer of Lebesgue Integration has been used successfully both in the classroom and for individual study. Bear presents a clear and simple introduction for those intent on further study in higher mathematics. Additionally, this book serves as a refresher providing new insight for those in the field. The author writes with an engaging, commonsense style that appeals to readers at all levels. Review: The First Book to Read on Lebesgue Measure! This book is exactly what it is advertised to be: an introduction to the Lebesgue measure and Lebesgue integral which will give the reader a solid foundation in the subject. I would recommend it to anyone as the first book to read on the subject, and it is particularly well suited for self study. For the self-study student, there's one small flaw in the book about which it is worth a note. In Problem_5 on page 5, in the review of the Riemann integral, the student is asked to prove that for a Riemann integrable function the upper and lower bounding functions converge to the function being integrated at all but a _countable_ set of points. As a counter example, consider a function which is 0 everywhere except on the Cantor set, on which it is 1. For any sequence of partitions, consider the (uncountable) set of points in the Cantor set less the (countable) set of points which are endpoints of the partitions. This is a minor point, and more importantly note that the result is true if "a countable set of points" is replaced with "a set of measure zero." Results like this are why the concept of measure is considered so powerful, and the fact that this book does so well in getting the student to think about these ideas is why I recommend it so highly! http://rapidshare.com/files/4207 ... gue.integration.pdf http://mihd.net/ujeot9 [ Last edited by laizuliang on 2007-10-31 at 16:25 ] |
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