I was recently talking to a well-known professor about what kind of math is used in theory research. He said, "The entire field of economics is coordinated around real analysis, but I have no idea why - I've never used it in research at all. What you actually need to know is proof-based linear algebra and probability theory (not necessarily measure-theoretic, although that doesn't hurt)."
No question here, just figured this information might be of value to someone.