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I want to self study real analysis. So far, finished the first seven chapters of Baby Rudin (up to and including sequences and series of functions) and now want to proceed into more advanced books.

I have couple options, including

  • Stein&Shakarchi
  • Folland
  • Royden
  • Rudin's Real&Complex Analysis
  • Kolmogorov-Fomin

Among these five (also happy to hear if you have further recommendations) which are more accessible and has better treatment of the material? I'm especially thinking among first three, so if there would be a comparative answer for the first three books, I would be really happy. Any help is appreciated. Thank you!

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The first two books you listed are excellent, and it may be worth reading the two together. Stein's book (at least in the first three chapters) focuses on Lebesgue measure in $\mathbb{R}^n$, while Folland takes a more general, abstract approach. It can be useful to have a concrete special case to think about when learning the general theory. There's a similar contrast in the functional analysis sections of the two books: Stein focuses on the simpler case of Hilbert spaces but goes into more depth, while Folland says more about the more general theory of Banach spaces.

The real analysis portion of big Rudin covers more or less the same ground as Folland. I prefer Folland, but big Rudin is also a good book.

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