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QUESTION
Suppose (f_n) is a sequence of functions, each continuous on [a, b] and differentiable on [a, b]. Suppose that the sequences (f_n) and (f'_n ) are...
Suppose (f_n) is a sequence of functions, each continuous on [a, b] and differentiable on [a, b]. Suppose that the sequences (f_n) and (f'_n ) are uniformly bounded on [a, b]. Prove that (f_n) has a uniformly convergent subsequence.
