Real Analysis (4th Edition) 4th Edition by Halsey Royden (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐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

⭐Unfortunately, adding Fitpatrick to the authorship of this previously wonderful real analysis text did not benefit anyone–at least in the fourth edition, first printing. There were more errata in this text than I’ve ever seen in any other text. It makes you wonder if anyone was checking the text before it was published. I’m hoping later printings improved, but my professor, classmates, and I did not appreciate being beta testers. Unfortunately, because of the state of this text, the professors who loved and used Royden at my graduate school have since switched to Folland for all future real analysis course. It’s quite a shame, and I’m not sure Mr. Royden would have been pleased.

⭐Foolishly I originally opted for what turned out to be a paperback copy of the 3rd Edition of “Royden” thinking that I would be closer to the original. Well, not everybody makes the right decision right away. I have since learned that Royden passed away suddenly back in 1993. This explains why for some time no new edition of this classic book came out, not since 1988. This might also explain why the paperback 3rd Edition is so poorly typeset. Rest assured, the 4th Edition with Fitzpatrick has been marvelously typeset.When I studied Real Analysis the course textbook was Principles of Mathematical Analysis by Rudin.However, I used Royden as one of my reference texts for Graduate Probability One. Fitzpatrick has added to the material in Royden by making corrections and finishing proofs. I take these edits to be reliable. But one has to admit that the book is always going to be referred to simply as Royden, in the same way that American league referees occasionally refer to Indianapolis as Baltimore.

⭐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.

⭐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.

⭐Was not a new copy as stated or the same printing as is pictured on the sale. Despite this, the book is in reasonably quality and has no glaring issues.

⭐This book is good for people who have already don’t some graduate real analysis. How ever this book has more problems which is a plus and few text errors. But this book is overall not bad. But don’t get me wrong. Material is super tough. But that’s why we do it 🙂 good luck everyone .

⭐For some reason Royden covers measure theory and integration twice: first for Lebesgue measure, and then for general measures later on in a separate chapter much further into the book. I’m not sure why he decided to repeat all the same results and theorems. Personally, I think Rudin’s text does a better job with measure theory.

⭐It’s not the United States Edition, the book is for saling in the “poor countries” so it’s quality is down …

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