STEM grad student. Currently sitting in a course that talks about PDE at the level of Evans’ book chapters 5-7. The FA that are needed are supplied in the course, with lebesgue integration used as a black box.

I realized that I might benefit from knowing some more abstract results on operator theory and topologies that are not particularly ‘immediately useful to PDEs’, but for certain engineering applications.

How doable is to take an abstract FA course without grad level real analysis (measure theory). Is it a better use of my time to self study materials instead?