Rudin's PMA isn't just real analysis; the entire book is basically written in the context of complex numbers. I love Baby Rudin, because even though it's a very tough book (he doesn't spoon feed you at all) and even though the exercises are very challenging, it's basically impeccable (aside from the measure theory/lebesgue integral chapter) and has definitely stood the test of time. Apostol is okay too, but I don't like his treatment of Lebesgue measure and Lebesgue integration (he manages to only define "measure zero"; you never learn what measure actually is! and measure theory is important)
I would recommend Zygmund and Wheeden's Measure and Integral. The book goes through most of the important results of analysis and does a thorough treatment of Lebesgue measure and integral.