Consider the Cantor function F:[0,1]→[0,1], and set f(x):= x+F(... | Filo
Consider the Cantor function F:[0,1]→[0,1], and set f(x):= x+F(... …
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Let c be the Cantor function defined on [0,1]. By using integra... | Filo
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Let P be the Cantor set constructed in Sec. 2.44. Let f be a bounded real function on [0,1] which is continuous at every point outside P. Prove that f ∈ℛ 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 . | Numerade
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