Let be a sequence of functions that converges uniformly to on A and that satisfies for all and all .
If is continuous on the interval show that the sequence converges uniformly to on .
Can anyone give me some hints to start the proof?
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Originally Posted by problem Can anyone give me some hints to start the proof? Notice that g is uniformly continuous (as a continuous function on a bounded interval is uniformly continuous). Pick an epsilon, then for some such that . Now what does uniform convergence of the f_n tell you about large enough n?
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