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I am thinking of self studying the first six chapters of Folland's Real Analysis: Modern techniques and Their Applications. I had read the first six chapters of Baby Rudin in the first real analysis course I had taken and would love to hear what people think of Folland's book for a second real analysis course. Has anyone read this book as an undergraduate? Is it too challenging for an undergraduate student?

Bonus: Does anyone have any other suggestions for a different textbook that can be used in a second semester of real analysis? I've read about Spivak's book but I don't think a physics-based analysis course is relevant to me (I want to pursue graduate-level statistics in a couple years).

Edit: I would love to learn some measure theory.

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  • $\begingroup$ what kinds of topics do you wish to cover? Folland's text is probably a good idea (I don't have much experience, so I can't really comment about it) $\endgroup$ – peek-a-boo Apr 30 at 5:04
  • $\begingroup$ I think multivariable calculus (differential and integral calculus, atleast the basics) is definitely a must. If not, any book on Lebesuge integration might be a good fit (Folland's is something I see highly recommended) Currently, I'm working through Amann and Escher's Volume III of Analyisis, and I like their very general approach to measure theory and integration (and eventually its use in developing integration on manifolds). $\endgroup$ – peek-a-boo Apr 30 at 5:11
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    $\begingroup$ I think it's a great book on measure theory that takes a fairly abstract approach. (Great in some ways, but not great at motivating things.) You're ready for it, and if you don't like it you can just switch to a different book. No need to commit to a particular textbook. You might want to complement it with a book that takes a more concrete approach to developing Lebesgue integration, such as Zygmund and Wheeden or Royden. Sheldon's Axler's new book on real analysis looks good. $\endgroup$ – littleO Apr 30 at 5:20
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    $\begingroup$ It's been a long time since I read Folland, but in my memory it is very good but a bit terse - occasionally lacking motivation and seeming a little too optimized for short proofs. I found Stein and Shakarchi to be a little more readable. But you can't go wrong with either, really. $\endgroup$ – Jair Taylor Apr 30 at 5:29
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    $\begingroup$ My new book Measure, Integration & Real Analysis may suit your needs well. The electronic version of the book is available for free at link.springer.com/content/pdf/10.1007%2F978-3-030-33143-6.pdf . $\endgroup$ – Sheldon Axler May 1 at 4:42
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Has anyone read this book as an undergraduate? Is it too challenging for an undergraduate student?

I personally read Folland after Baby Rudin. If you think the style of Baby Rudin is good for you, then you should be able to read Folland.

However, I think you should go a bit further in Baby Rudin before learning measure theory. Chapter 7 and 8 are typically taught in first year analysis courses.

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  • $\begingroup$ Can you please elaborate on why you are suggesting that I read chapters 7 and 8 of Baby Rudin before reading measure theory? $\endgroup$ – Ricky_Nelson Apr 30 at 6:22
  • $\begingroup$ @Ricky_Nelson Chapters 7 and 8 of Baby Rudin covers things like uniform convergence and Fourier series. I would say uniform convergence is a prerequisite to study things like convergence in measure in measure theory. Fourier series gives a basic example of an orthogonal basis of a Hilbert space, an object studied in functional analysis. $\endgroup$ – RunningMeatball Apr 30 at 16:44
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It isn't too challenging for an undergraduate. I remember it being quite impressive. I did some advanced things as an undergraduate; I was at Berkeley and got honors in mathematics. I've forgotten a lot of things, but I do remember the book fondly, and for one thing, I learned about generalized Cantor sets in there. I recommend working out with it if you're interested in real analysis. It's a good reference to have around also.

I took real analysis my first year in grad school. I think we used Wheeden and Zygmund. They should have some material on measure theory.

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