Measure theory will be useful for the econometrics sequence. Inverse and implicit function theorems are integral - pardon the pun - to micro I.
My analysis professor was pretty slow and didn't cover much of the tail end of a normal yearlong analysis sequence (Lebesgue integration and measure theory, Riemann integration in R^n, inverse and implicit function theorems). Are any of these topics particularly crucial to the first year econ sequence? I'm planning to take the first year sequence next year, so if there are deficiencies caused by this I want to remedy them.
I'd recommend looking up course materials for the first sequence at your university (notes, psets, maybe even exams are often available on professor's websites). The relevance of these topics may vary by institution, even within a similar ranking range.
I'm at top 5-7 now (therealslimkt if I remember right you're UG at a similar institution). I would say Lebesgue integration and measure theory would perhaps give you more insight to some of the topics covered, but are far from necessary or important to have coming in. Inverse and implicit function theorems counted for one question on one midterm for us, though my impression is this certainly varies by program.
In short, knowing these topics will generally help you gain a more insightful understanding of material, but I would doubt that missing them ahead of time will significantly impact your ability to do well. But check for course notes to get a better sense.
Also.. Consider taking a field course instead of the full first year sequence (especially in place of macro, if that's not your field of interest)? Taking even one of first year micro or metrics and doing well (an A) is a pretty good signal already. Beyond that, it might be worth spending your time developing your research interests. You'll cover all of first year again, anyway.
You know best for you, but food for thought.
Appreciate the advice, jjrousseau! I've actually taken some field courses already and plan to take more. I also meant first year micro sequence + first semester metrics, since I'm potentially interested in micro theory. And yes I'll check out course notes to see what's specific to my university.
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