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nhamann comments on Learning the foundations of math - Less Wrong

4 Post author: jsalvatier 24 October 2010 07:29PM

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Comment author: nhamann 25 October 2010 12:49:31AM *  1 point [-]

So it looks like you're interested in learning the fundamentals of classical logic and set theory, and then paving your way towards measure theory. If you don't have a solid background in set theory, then you probably don't have a strong background in real analysis either, which to my understanding is needed for measure theory. (I don't know how you can do measure theory without even knowing what the Riemann integral is).

You should take a look at Real mathematical analysis by Pugh. You're going to need to know basic stuff like basic set theory and functions and such as a prereq, but it's a very lucid introduction to real analysis with metric space topology and compactness and connectedness and all that. It was the first book I found that had a good explanation of Dedekind cuts (Rudin's Principles of Mathematical Analysis has a very terse description. Pugh, on the other hand, has pictures!)

For measure theory, I haven't read very far through them but here is a 4-volume set on Measure theory available for free online from D.H. Fremlin. It has some introductory set theory stuff if I recall, which might be a good starting point if your grasp on logic is strong enough.

For basic logic, How to Prove It: A Structured Approach by Velleman is my personal favorite.