- For integration I will use a heavily modified version of (Jan) Mikusinski's approach which you can find in Debnaith and (Piotr) Mikusinski ``An introduction to Hilbert spaces with applications'' (Academic Press)
- A nice reference for Hilbert spaces is G.F. Simmons ``Introduction to Topology and Modern Analysis''
- You might like to look at P. Halmos' ``A Hilbert space problem book''
- A good over-all reference, a little more advanced than this course, is P.D. Lax's book ``Functional Analysis'' (Wiley-Interscience) -- a nice book to have.