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^ Ebook Free Real Analysis, 3rd Edition, by Halsey Royden

Ebook Free Real Analysis, 3rd Edition, by Halsey Royden

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Real Analysis, 3rd Edition, by Halsey Royden

Real Analysis, 3rd Edition, by Halsey Royden



Real Analysis, 3rd Edition, by Halsey Royden

Ebook Free Real Analysis, 3rd Edition, by Halsey Royden

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Real Analysis, 3rd Edition, by Halsey Royden

This is the classic introductory graduate text. Heart of the book is measure theory and Lebesque integration.

  • Sales Rank: #201505 in Books
  • Published on: 1988-02-12
  • Ingredients: Example Ingredients
  • Original language: English
  • Number of items: 1
  • Dimensions: 9.20" h x 1.10" w x 5.90" l, 1.40 pounds
  • Binding: Hardcover
  • 444 pages

From the Publisher
This is the classic introductory graduate text.

Most helpful customer reviews

0 of 0 people found the following review helpful.
A classic in real analysis.
By J. Rogelio
This book, as far as I consider it, is a classic. Although it has some errata and stuff, it is one of the best books ever written in Real Analysis. I am happy to managed get this specific edition since the author didn't manage to publish its fourth edition, while it was Fitz Patrick the one who edited that edition. I think that books are more valuable when the authors are the only ones who edit them, otherwise I don't think they're worth reading. At least that's my opinion.

Then, about the book, it takes to know some modern algebra, set theory and basic analysis to study from this fine book. I haven't seen a book that specially teaches Daniell's integral and this one does. The book is rich on references where one could further study material related to real analysis to the higher level. I think this book will be very useful to serious mathematicians and to those self-studying guys who love the rigour.

24 of 26 people found the following review helpful.
Classic text on measure & integration theory
By Alexander C. Zorach
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.

21 of 23 people found the following review helpful.
Maybe good as a supplement, or a first time looking at the material
By C. Dolan
There are three books that are usually used for a first graduate course in analysis, including measure theory, namely Rudin's Real and Complex Analysis, Folland's Real Analysis, and Royden's book. Of the three, I would say Royden's book is the easiest, both in terms of the exposition, material, and exercises. Of the three, Royden is the only one to fully develop the Lebesgue measure and the associated integral before developing a more general theory of measure and integration. Furthermore, he does not develop Hilbert and Banach space theory, the very basics of functional analysis, to anywhere near the extent that Folland and Rudin do.

There is some debate as to whether it is better to start with the Lebesgue integral, and then talk about abstract integration, or the other way around. Personally, I found the development of the Lebesgue integral a bit tedious; the whole thing works a bit better when you first talk about abstract integration, which really isn't a terribly difficult concept, prove the basic integration theorems, then show how to construct an outer measure, and suddenly, the Lebesgue measure and integral just falls into place. I'm not sure anything is lost in the process.

The biggest shortcoming in this book would have to be the exercises: for the most part, they are not very difficult, particularly when you compare them to say, Rudin's text. For the most part, the exercises are fairly trivial, and if they are difficult, or require a bit of creativity, Royden often gives you lots and lots of hand-holding, sometimes even in the form of sketching out the proof for you. In spite of the relatively low difficulty level, most of the exercises are fairly instructive, in so far as they highlight, elucidate, and expand upon the material.

For the most part, this book is not bad. It makes a good supplement to a book like Rudin or Folland, as it is less abstract, and does a better job motivating the material. The exercises here can work well if you want some extra practice that won't take up too much time. If you're a student of econ, or physics, or you just feel like learning graduate-level real analysis, then this book is probably adequate (although I should qualify that statement by saying that I know nothing of econ and little of physics). But if you are a serious student of mathematics, particularly the pure variety, this is really not the book you should be using. It is just too easy.

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