 Quote by bdforbes
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Folland doesn't required any prior familiarity with Lebesgue integration as long as the reader is willing to accept a few results (e.g., Lebesgue dominated convergence theorem) without proof.
 Quote by bdforbes
Unfortunately my library doesn't have either text but I will look elsewhere.
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If you want, you probably can get Appel through inter-library loan. Although not as rigourous as Folland, it is a very interesting book,
http://press.princeton.edu/titles/8452.html,
and it is still much more rigourous than many physics books. Its treatment of Green's functions starts with a pedagogical example of the Green's functions for a driven harmonic oscillator (I think; out of town right now so I'm not sure) that is basic, but illuminating.