I have completed two courses in real analysis that covered up to chapter 9 in Rudin's Principle of Mathematical Analysis (and one on complex analysis). So if I am interested in continuing on in analysis (real analysis and not complex analysis), what would be a good direction to go from here? What would be a good book to learn from? As my interest is primarily number theory I was wondering if there is a direction in analysis that would be helpful in this aspect.
Recommendations for real analysis
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0Complex analysis is certainly useful when dealing with number theory. – 2012-06-14
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0@FernandoMartin As you can see in the question, I've done some complex analysis and I'm looking to foray into real analysis. – 2012-06-14
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1Perhaps learn enough ergodic theory to be able to handle its number-theoretic application. – 2012-06-14
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0@AndréNicolas That is a very good suggestion. I didn't think of that. Thanks! – 2012-06-14
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0@AndréNicolas I really like your suggestion on ergodic theory best. Do you mind putting your comment as an answer so that I can accept it? – 2012-06-15
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0I think there are a number of good suggestions. The comment did its job drawing your attention to the subject! – 2012-06-15