>>14002164You should be comfortable with basic real analysis. Sequences of functions appear everywhere and you should know the basics of sequences and series of functions/real numbers. Understanding stuff about continuity and differentiability, while not always directly required, is standard literacy at this point.
As a bit of a tangent: Exposure to the Darboux/Riemann integral makes sense but isn't really required either since a different theory of integration is built up, and then this is related to Darboux/Riemann integrals. The main advantage of Darboux/Riemann integrals is that the fundamental theorem of calculus is fairly easy to formulate and prove. The theory of integration arising from measures (the one most closely identifiable with the Darboux/Riemann integral is the Lebesgue integral) is otherwise superior, and has pretty effortless conditions for moving limits into integrals and swapping integrals. Since series are actually just integrals over the natural numbers wrt the counting measure, this theory of integration also gives a shitton of stuff for infinite series. Very cool stuff.
Another thing that'll help is being comfortable with handling sets, which might come from a course in set theory or topology. I don't think the required level is that high but it often seems to confuse people.
I really like Cohn's Measure Theory and I think it is an excellent introduction. The prerequisites are light.
