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Having taken Real Analysis I before (the seven first chapters of baby Rudin) I have the option to take Measure Theory now. However I am torn between that and Set Theory. Which course would you go for first? Which theory would give me a better grounding in Mathematics?

Thank you

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    $\begingroup$ I think they are both useful, but set theory is more applicable even outside of analysis. $\endgroup$
    – IAmNoOne
    Commented Apr 24, 2014 at 23:21
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    $\begingroup$ Set theory might also pique your interest in philosophy as well. $\endgroup$ Commented Apr 24, 2014 at 23:48
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    $\begingroup$ Verify it for yourself, but it is my impression that there is much more of the mathematical literature that uses the ideas of measure theory than use those of axiomatic set theory. Assuming you don't intend to be a specialist in either field, I recommend taking the course in measure theory and read a good book on set theory on your own for fun. $\endgroup$ Commented May 1, 2014 at 5:35
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    $\begingroup$ I don't know if it means much if anything, but you will get many more hits on Google and Google Scholar for "Lebesgue measure" than for "zfc set theory." $\endgroup$ Commented May 1, 2014 at 5:55
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    $\begingroup$ But of course you must take BOTH courses and many others as well. What's your problem? Do you only have three months left to live? $\endgroup$
    – Wd Fusroy
    Commented Aug 29, 2019 at 18:54

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I would recommend taking set theory as it gives you a good grounding in the fundamentals of modern mathematics. For me, learning axiomatic set theory gave me a better understanding of the real core of mathematics, but that's just my personal experience, to others it may seem very dry.

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I think it depends a great deal on what you want to do. People that are very concerned with foundations and logic would probably say to go for the course in set theory, while more application-oriented people (and here I'm including applications to other areas of mathematics, not simply mathematics applied to the "real world") might say measure theory, depending on their point of view.

I assume there's some reason you can't take both courses if you're asking this question, but would it be possible to officially take one course and then sit in on the other? If you want to go on to learn more about areas that will apply measure theory (e.g., dynamical systems & ergodic theory, functional analysis, ...), then I would say go ahead and take measure theory.

If you have the option of taking both courses at a later date, though, maybe set theory would make the most sense right now since, as Jón said, it will give you some foundations for other more general things later.

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