Integral Question with Cantor Set
Exercise 6 in Chapter 6 of Baby Rudin is giving me some difficulties..
Let P be the Cantor set. Let f be a bounded real function on [0,1] which is continuous at every point outside P. Prove that f is Riemann integrable on [0,1].(Hint: P can be covered by finitely many segments whose total length can be made as small as desired. Proceed as in Theorem 6.10.)
I understand that their total length will be (2/3)^n and therefore we can show that the total length is less than epsilon by taking n sufficiently large, but how do we cover each interval in the set with finitely many segments when it is infinite..? I mean it seems like the total damage will be negligible and won't affect the integral, but I'm confused about how to go about this. Any help would be greatly appreciated, thank you.