Textbook (Paperback - REV)
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September 02, 2005: I have been a student of Analysis for several years and have done research in PDE's and mathematical physics as well as TA'd PDE's and analysis courses and let me tell you...This book is an aweful treatment of this beautiful subject. I admit that some students respond well to the concise (but boring) exposition but this subject is really capable of coming to life. Royden convinces the first time reader otherwise. Professors who choose this book to teach from are most likely as insipid as it. Not recommended.
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February 07, 2001: This is a wonderful book from which to learn real analysis. It is one of the few texts that first treats Lebesgue measure on R before presenting general measure theory. That makes it much easier to learn. The exercises are also pretty hard, and that is a good thing.