I've been thinking of buying books from amazon to self-study analysis. I find a lot of positive/negative reviews about either Rudin (too difficult), or Abbott (too basic) plus Kolmogorov book: Kolmogorov book. It is for self study.
I am not a mathematics major, I am computer science student, who deals with a lot of probability in machine learning. I would like to study analysis (or rather measure theory but as I understand it is part of analysis) to apply to this particular field, and to exercise to write simple proofs, and understand articles dealing with epsilons and sets (i can do basic ones from strang linear algebra and multivariable calculus courses, and geometry at school) and I would like to understand probabilistic articles on Wiki that deal with real analysis.
So can someone familiar with both options (Rudin vs abbott + Kolmogorov) advise which one is better in this regard?
Or maybe there is some other book I don't know of - but everywhere I go it is always Rudin.
This question is different from similar ones here because field of application of real analysis is gonna be probability.
PS. Thank you for recommendations here. I decided to go with Abbott for the beginning and then continue with Folland/Rudin, where the second one I found at my university library. Maybe will take a year/1.5 all in all :)