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Real Analysis (3rd Edition) | 
 enlarge | Author: Halsey Royden
Publisher: Prentice Hall
Category: Book
List Price: $143.40
Buy New: $108.89
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Rating:  22 reviews
Sales Rank: 51069
Media: Hardcover
Edition: 3
Pages: 434
Number Of Items: 1
Shipping Weight (lbs): 2.1
Dimensions (in): 9.3 x 6.3 x 1.6
ISBN: 0024041513
Dewey Decimal Number: 515.8
EAN: 9780024041517
Publication Date: February 12, 1988
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| Customer Reviews: Read 17 more reviews...
 Classic text on measure & integration theory August 22, 2006
Alexander C. Zorach (New Haven, CT)
13 out of 13 found this review helpful
Many people criticize this book as unclear and unnecessarily abstract, but I think these comments are more appropriately directed at the subject than at this book and its particular presentation. I find this classic to be one of the best books on measure theory and Lebesgue integration, a difficult and very abstract topic. Royden provides strong motivatation for the material, and he helps the reader to develop good intuition. I find the proofs and equations exceptionally easy to follow; they are concise but they do not omit as many details as some authors (i.e. Rudin). Royden makes excellent use of notation, choosing to use it when it clarifies and no more--leaving explanations in words when they are clearer. The index and table of notation are excellent and contribute to this book's usefulness as a reference.
The construction of Lebesgue measure and development of Lebesgue integration is very clear. Exercises are integrated into the text and are rather straightforward and not particularly difficult. It is necessary to work the problems, however, to get a full understanding of the material. There are not many exercises but they often contain crucial concepts and results.
This book contains a lot of background material that most readers will either know already or find in other books, but often the material is presented with an eye towards measure and integration theory. The first two chapters are concise review of set theory and the structure of the real line, but they emphasize different sorts of points from what one would encounter in a basic advanced calculus book. Similarly, the material on abstract spaces leads naturally into the abstract development of measure and integration theory.
This book would be an excellent textbook for a course, and I think it would be suitable for self-study as well. Reading and understanding this book, and working most of the problems is not an unreachable goal as it is with many books at this level. This book does require a strong background, however. Due to the difficult nature of the material I think it would be unwise to try to learn this stuff without a strong background in analysis or advanced calculus. A student finding all this book too difficult, or wanting a slower approach, might want to examine the book "An Introduction to Measure and Integration" by Inder K. Rana, but be warned: read my review of that book before getting it.
this book is just plain good. July 23, 2003
Tim (Melbourne, Florida USA)
11 out of 17 found this review helpful
I began as a graduate student in applied maths less than a year ago; all of the students that I spoke with prior to that said that real analysis with rudin's book was their worse & hardest class..
So when I walked into MTH 5111 Real Variables I thought oh *&^% what am I in for?? but then I picked up the Royden book and I understood the way he was presenting the materail.. the book is very stright to the point + leaves channelgning problems to the HW sets but the autor clearly outlines. I have learned more from this book and course than any other...
Readable, very well written May 11, 2002
Professor Joseph L. McCauley (Austria+Texas)
9 out of 16 found this review helpful
With basic knowledge of point set theory, a mathematically-oriented physics student can use this book for self-study. I used it as advanced grad student to learn measure theory and Lesbesgue integration. I certainly remained a beginner (surely could not have passed a typical math exam in analysis) but was nevertheless able to apply the basic ideas of meassure theory some decades later to resolve a subtle question about fractals.
terrific reference book June 28, 2002
7 out of 10 found this review helpful
I'm surprised to see some negative reviews for this book. I've long found it to be an extremely useful reference book and probably look more stuff up in this book than any other math book I own. Anyone who works with real analysis but is not an expert on the topic would find this useful.
A Standard Text March 20, 1999
6 out of 10 found this review helpful
If you are going to study mathematics at the graduate level, your analysis book will likely be or have been Royden. The subject topics include the L.O.M, generalized measure theory, convergence theorems and the Radon-Nikodym (all in one semester).
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