Real Analysis Book Choice

Question

I am currently planning to get a book on Real Analysis for self studying before diving into my 4th year real analysis course. The standard textbook for my 4th year course is Stein's Measure, but I do not like much about abstract measure introduced near the end. Perhaps because I am currently taking 3rd year real analysis course in the level of Pugh with some other additional materials.

Anyway, I am considering one of the followings: Folland - Real Analysis, Bruckner, Bruckner, Thomson - Real Analysis, Yeh - Real Analysis, Kantorovitz - Introduction to Modern Analysis (and maybe Cohn - Measure Theory)

(Note: Royden is omitted because I am waiting for 2nd printing and waiting so that I can get it cheap from some website (like abebooks), so 12 pages of erratas are all fixed)

Which book do you think is most suitable for self-study? (My 4th year course is cross-listed, meaning it is equivalent to first year graduate real analysis course)

Answer 1

One of the very best books on analysis, which also contains so much more then just measure and integration theory,is available very cheap from Dover Books: General Theory Of Functions And Integration by Angus Taylor. You can probably get a used copy for 2 bucks or less and it contains everything you ever wanted to know about not only measure and integration theory, but point set topology on Euclidean spaces. It also has some of the best exercises I've ever seen and all come with fantastic hints. This is my favorite book on analysis and I think you'll find it immensely helpful for not only integration theory, but a whole lot more.I don't know if it's available where you live,but you can probably get it incredibly cheap online. I strongly encourage you to find a copy-I think you'll find it immensely helpful. I think this book should be mandatory summer reading before a graduate analysis course based on Big Rudin- I think students would find Rudin far less difficult after spending a few weeks working through Taylor's classic.

Answer 2

How about Walter Rudin's Real and Complex Analysis and Theory of Functions by Edward Charles Titchmarsh. These two books have rather different styles, both cover measure theory. The first is rather abstract and the later is written with the old school hard analysis style. I do highly recommend the later, the first one is a best seller.

Answer 3

If you want an interesting alternative that goes deep into why things work out as they do in real analysis, especially things like sound and convincing explanations of Lebesgue Measure, then take a look at Terence Tao's 2-volume Analysis textbook.

Answer 4

I recommend Klambauer's Real Analysis from Dover especially for its clear presentation of the Lebesgue measure and integral. It uses Royden's strategy of working on the real line first, generalizing later.