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Feb28-12, 05:18 AM
micromass's Avatar
P: 18,299
Quote Quote by Chsoviz0716 View Post
Thank you everybody who replied. I looked up the books mentioned above and was a bit puzzled.
Some books like Rudin's PMA or Apostol's cover the basic materials such as sequences or differentiation or Rieman-Stieltjes integration, while some other books I found cover very little of those, but cover measure theory or Lebesgue integration in more detail.
Should I conclude that there are two types of real analysis books; easier ones(the ones I mentioned first) and relatively hard ones(the latter)? Or is it going too far to distinguish those books into different categories?
Uuuh, you'd be the first one who would call Rudin an easier book...

But yes, there are differences between lots of real analysis books. You will most likely have to read multiple books on the subject.
In any case, I don't think it's worth it to waste much time on Riemann integration. Riemann integration is such a stupid and flawed method compared to the other things we have. The faster you cover Lebesgue, the better in my opinion.