![]() My only complaints are that some of the later proofs are hard to read, and there is sadly no discussion of the spectral theorem. Also, the exercises are abundant and uniformly fantastic. The early material is covered with all the appropriate detail, while the later material quickly provides the essential definitions and results needed to come to grips with an unfamiliar idea in the literature. ![]() Iam also very grateful to the many anonymous referees who made several corrections and suggested many important improvements to the text. They didnt ask any real or complex analysis, but I guess from my handling. Second Edition we will also use Stein-Shakarchi’s Real Analysis as a supplementary text. Bartle & Sherbert's Introduction to Real Analysis. the real analysis course corrected several errors in the lectures notes fromwhichthistextisderived,andgaveothervaluablefeedback. Terry Taos generals My examiners were Stein, Kleinermann and Rudnick. It has the most comprehensive swath of applications of analysis of any introductory text I have ever encountered: basic functional analysis, Fourier theory, probability theory, distributions, Hausdorff measures, Haar measure, smooth measures, and more. Terence Tao's Analysis I and II (go into a lot of detail while maintaining high readability) Stephen Abbott's Understanding Analysis. ![]() I am not yet all that experienced (I just finished my third year of graduate school), but overall I have gotten more use out of this book than any other that I own. Nobody has mentioned Folland's "Real Analysis with Applications"? This was the textbook for my undergraduate real analysis course (measure theory, Banach spaces, Hilbert spaces), and I still go back to it all the time. ![]()
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