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Here on the site there are already some questions asking for suggestions of real analysis books. By way of reference I will cite a few questions. [1], [2], [3] and [4].

What I want to ask is not a suggestion from a real analysis book, as there are already great recommendations in the questions above. But suggestions for "parts of books" (or lecture notes, videos, posts, etc...).

Well, when we think about book suggestions, we choose those that on the whole are very good, what I'm asking for are suggestions where the material is superior than others on a specific topic or that you found the way of treating some subject interesting. It doesn't have to be a material in itself, but also, examples that you found in just some materials, comments, interesting theorems that are not in all materials and even different exercises. And how these suggestions can help in understanding the subject.

And finally, it has some suggestions for more modern concepts/theorems/applications, being that, for example, the most recommended book is by Rudin, which is from 76 (3rd edition), maybe there are things missing from these books that you find important.

To clarify, consider an actual analysis book that covers: set theory, countability, real numbers, sequences and series, topology of the real line, limits of functions, continuity, derivative, integral (riemann) and sequence and series of functions.

Edit: I don't think this is an opinion-based question so much as a book suggestion. Because the suggestions I asked for must have some basis. A single example, but it has to be somehow relevant.... A book treating a subject better than others... etc

Mrcrg
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    I like the section on the spectral theorem in Strichartz' Way of Analysis. In the same book, the development of $\sin x$ and $\cos x$ is also excellent. – Andrew Jun 26 '23 at 21:59
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    What is the context behind your question? – Rob Arthan Jun 26 '23 at 22:42
  • @RobArthan It's more curiosity. When I prepare analysis monitoring, I end up doing this, taking demonstrations in book X, example from book Y, exercises from another .... – Mrcrg Jun 26 '23 at 22:49

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