What are the best books to self study real analysis? I am a physics masters student and am looking forward to study representation theory. I want to study the real analysis I need for studying functional analysis.
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For self-study, I strongly recommend Abbott's "Understanding Analysis". He does an excellent job of motivating the abstract concepts and introducing the frequently unintuitive behavior of infinite sets and processes.
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$\begingroup$ Any recommendations for functional analysis? $\endgroup$ Dec 12, 2018 at 17:03
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$\begingroup$ functional analysis (and other modern math topics) --- Introductory Functional Analysis with Applications by Erwin Kreyszig (1978) AND Introduction to Topology and Modern Analysis by George F. Simmons (1963) AND the books here AND Paul Roman's 2-volume work Some Modern Mathematics for Physicists and Other Outsiders Volume 1 contents. $\endgroup$ Dec 12, 2018 at 19:51
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$\begingroup$ We used Folland's "Real Analysis" in my graduate RA class, but I found that I wanted more of a Topology/Measure Theory background to really understand it. You might find some useful comments at this discussion: math.stackexchange.com/questions/3025828/… $\endgroup$ Dec 12, 2018 at 21:29