Real Analysis, Fourth Edition, covers the basic material that every reader should know in the classical theory of functions of a real variable, measure and integration theory, and some of the more important and elementary topics in general topology and normed linear space theory. This text assumes a general background in mathematics and familiarity with the fundamental concepts of analysis. Classical theory of functions, including the classical Banach spaces; General topology and the theory of general Banach spaces; Abstract treatment of measure and integration. For all readers interested in real analysis.
This can't be the best book out there...
By From Detroit on Oct 19, 2011
We're using this text for my real analysis class. We've made it through 8 chapters so far, and I must say that I'm rather disappointed with this book. I can't compare the 4th edition to any of the previous editions, as I haven't read them, but I'm not sure if this really could be called an improvement. It's riddled with errors (the errata, as of September 2011, is 12 pages long, and even it has errors! I've found some of the proofs to be confusing (for example, see his proof of Young's inequality... I find that using the convexity of the exponential is much clearer. Semi-frequently, I find myself digging through Stein and Shakarchi, Kolmogorov and Fomin or Bruckner, Bruckner and Thompson's Real Analysis book to figure out what's going on. Professors: If you're going to require a text that costs this much, make sure it has less errors. Students: It's not just the reading that's flawed! Several exercises have typos, or are even completely misstated! Here's a link to the errata: [...] *Apparently the link was removed by someone that wasn't me. I suspect that it caused some red flags for Amazon to have an external link here. One can easily find it by typing "Royden Errata 4th Edition" in any search engine. 1/14/2012
A big improvement over 3rd Edition
By Progearstorm on May 22, 2013
When I found out that my class for real analysis would be using Royden, having used the 3rd edition long ago, I lost all hope for things turning out well. Short version: that book is awful for a student trying to learn the subject from scratch. Luckily, this is 4th Edition. It turns out measure theory isn't that hard! This time the proofs are clear, examples are sufficient, and there are more than enough problems. It's almost impossible to compare the editions. That said, there are two problems that keep this from being a five-star book. First, check out the errata. Lots of mistakes. Second, the publisher let through a bunch of copies that had broken typesetting, so watch out for that. They evidently didn't recompile their TeX when they should have, so in some copies (my original included) the references will be question marks instead of equation or theorem numbers. As you can guess, it is not helpful to be referred to theorem ?? or be told in a problem to justify equation ??. Overall it's a very good book, but there's a lot to watch out for. If you keep the errata nearby and make sure you didn't get a bad copy, you too can be thankful that you're not using 3rd Edition.
Okay book, not okay print
By Nina on Feb 03, 2013
My Real Analysis class follows this book. However, when I ordered it and got it, I found out that I have a bad printout - when any previously used equations were mentioned, only (??) was in the text, some exercises were missing or numbered differently, and some paragraphs were also missing. Somehow, the book cover was the same as the 4th edition. The seller agreed to take the book back, but it was still inconvenient, and I met other people from my class who had the same problem.
Don't listen to the other reviews -- This is a spectacular book
By Mr. Robert Hannah on Mar 24, 2013
This book is excellent. The layout is clean, and the proofs are solid and short. Why are people so irrational in their reviews of textbooks? 2/5 stars? But still good enough be the main reference in a Harvard analysis course? 3/5 is not low enough for some people! who perhaps think that their opinion is more important than others and wish to skew the average in their direction by voting less stars than a book deserves... I believe I will do the opposite to balance out the universe (4.5 stars is what I would rate this book). I've been reading it for the last few months, and I have loved learning from it. Yes there are errors, but part of there reason for that is that some chapters contain over 70 questions! There are 22 chapters, so I'll let you "do the math" (I would estimate there are about 1000 questions, so maybe we should cut him a little slack??)... Often a textbook will have a terse list of errata simply because the author does not put much effort into correction of errors that people find... This text contains double or triple the number of questions found in Rudin, and doing questions is the only way to really learn something in maths. Personally I would recommend doing every single question (apart from trivial ones) to gain the most from this book. That being said, it's pretty expensive. I bought an international edition from AbeBooks.
If you have to buy it, buy the paperback.
By C.s. on Nov 11, 2014
Give one star just want to attract your attentions! DO NOT BUY THE HARDCOVER! I bought the hardcover version and my friend bought the paperback version. The paperback version is average. The hardcover version for this book is extremely poor in quality (paper quality and printing quality). The content of the book is just ok but sometimes we have no choice other than this book. But, seriously, keep away from the hard cover version. I have other hardcover textbooks and their quality are far better than the Royden;s Real Analysis 4th Edition.
nice book, but have some typos
By Alvin on Apr 23, 2014
I used this book in my second semester analysis class. I think the book does a good job laying out measure theory and Lebesgue integration, and materials about topological spaces can serve as complement reading of Munkres' book (I'm taking topology at the same time). However, there are some typos in the book and some of the questions and examples are wrong. For example, p43, q18 is wrong; p143 q9 is wrong because in Young's inequality there is equality iff a^p=b^q, and on the same page the last example is incorrect.
By Chuong Nguyen on Apr 16, 2014
I would give this book 5 star if it were not because of typos. I agree with the other review regarding typos: too many and the errata is 19 pages long. Almost every single page in every chapter has typos. Most typos are easy to fix, but there are some where you have to insert a paragraph to fix it. Lets hope for a fix in the next edition (I would buy it immediately.) There are some good books that are just as good as this one: Stein and Shakachi is better (just my taste), Tao's An introduction to Measure Theory is a good one too if you read it along with Stein and Shakachi since Tao wrote his book based on Stein and Shakachi (not really based on, but in the same approach and he has many awesome comment.) Thats being said, this is a good book to study but unfortunately, many typos keep it from perfect.
Very well revised
By Prdrgy on Mar 10, 2014
I bought every version of it--the 2nd, 3rd, and then this one. All old chapters in the 3rd version have been very well revised, and new chapters have been added. Dr. P.M. Fitzpatrick of the University of Maryland, College Park, did a very good job revising it, and Ch. 17-22 could serve as a summary of the prerequisite knowledge for a functional analysis course, too. Overall, I'm happy to have this new version. I'd give it a 4.5 to 5 stars.
The information on R^1 integration is nice and easy to follow but the number of errors ...
By Person on Nov 08, 2014
The information on R^1 integration is nice and easy to follow but the number of errors is totally unacceptable(19 pages as of errata). It appears no one proof-read the book. Knowing the number of errors I can't recommended anyone buy this edition.
Fitzpatrick Don't Speak So Goodly
By Ian Hogan on Nov 27, 2012
The grammatical errors induced from third to fourth edition are quite irksome. Also, in many proofs, key words and symbols are switched, changing the meaning. But, the third was an outstanding book and the fourth is still my best resource on the subject.