Originally Posted by

**Zilch**
Most courses on measure theory really just teach you the basic tools. Most parts of advanced mathematics use these tools without even mentioning them so in that sense it is a very basic course in the grand scheme of things.

I took an analysis course once during my undergrad and this was the syllabus :

Banach and Hilbert spaces, theorems of Hahn-Banach and Banach-Steinhaus, open mapping theorem,closed graph theorem, Fredholm theory, spectral theorem for compact self-adjoint operators, spectral theorem for bounded selfadjointoperators. Additional topics to be chosen from: Lorentz spaces and interpolation, Banach algebras and the Gelfandtheory, distributions and Sobolev spaces, The von Neumann-Schatten classes, symbolic calculus of Hilbert space operators,representation theory and harmonic analysis, semigroups of operators, Krein-Milman theorem, tensor products of Hilbert spacesand Banach spaces, fixed point theorems.

I think what cheatuheart was getting at is that most theory applicants would have had several courses like the one above.