(Rudin, Ch. 6, Exercise 6) Divide the unit interval [0, 1] into thirds and remove the open interval G,). What remains is a pair of closed intervals, each of them one-third as long as the original. For...

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Extracted text: (Rudin, Ch. 6, Exercise 6) Divide the unit interval [0, 1] into thirds and remove the open interval G,). What remains is a pair of closed intervals, each of them one-third as long as the original. For each of the remaining intervals, do this again, i.e., divide the interval into thirds and remove the open middle interval. Repeating the process over and over again, what is left in the limit is the Cantor middle-thirds set C. Let f : [0, 1]] → R be a bounded function that is continuous at every point in [0, 1] \ C. Show that f is Riemann integrable on [0, 1]. (Hint: Use the argument of Theorem 6.10 from Rudin).