So I decide to self-study the real analysis (measure theory, Banach space, etc.). Surprisingly, I found that Rudin-RCA is quite readable; it is less terse than his PMA. Although the required text for my introductory analysis course was PMA, I mostly studied from Hairer/Wanner's Analysis by Its History (I did not like PMA at all). Although I said readable, I do not know if I actually understand whole materials as I am middle of first chapter, and I already have topology background from Singer/Thorpe and Engelking. I actually like Rudin-RCA, but I am not sure if I am taking great risk as many experience people seem to not liking Rudin for learning...
Is Rudin-RCA suitable for a first introduction to the real analysis? Is it outdated? What should I know if I decide to study Rudin-RCA.
I am not planning to read the chapters in complex analysis as I am reading Barry Simon's excellent books in the complex analysis.
No, No, and No. True, all the statements and proofs are squeaky clean, but the exposition, IMHO, is completely unsuitable for educational purposes.
Specifically for measure theory, I would recommend Vulikh's Brief course in the theory of functions of a real variable. For Banach spaces, Kolmogorov and Fomin's Introductory Real Analysis.