I'm an undergraduate with some measure and integration theory background. The undergrad analysis course I took at my institution covered the equivalent of the first two chapters of Folland's Real Analysis (ie introductory measure theory constructions, the convergence theorems for Lebesgue intergrals and Fubini-Tonelli) along with parts of chapters 5 and 6 on Elementary Functional Analysis and Lp Spaces. I was told that with some preparation I could probably take the second semester graduate introductory course on Functional Analysis that follows the first semester measure theory course. However, I am not certain what exactly I am to focus on in my preparation. Currently, I intend to do:
1) Chapter 3 of Folland which covers the Lebesgue Differentiation and the Radon-Nikodym Theorems since this appears to be the one major area which the intro grad course covered but I didn't.
2) Review Point Set Topology from say, Munkres (I'm mostly familiar with this up till Arzela Ascoli and Stone-Weierstrass).
3) Read an undergrad book like Kreyzig's.
Is there anything else I should focus on?
The Functional Analysis course will be using Functional Analysis, Sobolev Spaces and Partial Differential Equations by Brezis. We probably won't cover the entire book.
Thanks in advance.