5. A sequence of functions fn is said to be uniformly bounded on a set E if...
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5. A sequence of functions fn is said to be uniformly bounded on a set E if and only if there is an M > 0 such that for all x E E and all n EN. If each f n is a bounded function on a set E and fn -+ f uniformly on E, prove that {fn} is uniformly bounded on E and f is a bounded function on E.
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