Question: Let E be a nonempty subset of R and f be a real-valued function defined on E. Suppose that fn is a sequence of bounded

Let E be a nonempty subset of R and f be a real-valued function defined on E. Suppose that fn is a sequence of bounded functions on E which converges to f uniformly on E. Prove that

uniformly on E as n †’ ˆž (compare with Exercise 6.1.9).

fi(x) +..+ fn(x) f(x)

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