A sequence of functions fn is said to be uniformly bounded on a set E if and
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Suppose that for each n ∈ N, fn: E → R is bounded. If fn → f uniformly on E, as n → N, prove that {fn} is uniformly bounded on E and f is a bounded function on E.
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Choose N so large that fx f n x 1 for all x E and n N Set M supx2E ...View the full answer
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