I am curious about which areas of mathematics one should be comfortable with before learning QFT. I am familiar with the "learn-it-as-you-go" approach often advocated in physics, but would like to know how to avoid that in learning QFT. Naming of specific textbooks is appreciated.
(For the sake of this discussion, "learning QFT" can be taken to mean "learning at the level of/from Peskin and Schroeder's text.")
In particular, I would like to know what, in addition to the material in Rudin's Real and Complex Analysis, one should know. Would this be sufficient? How about Folland's Real Analysis?