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QID: #13514
Solution for QID #13514: Let f : R → R be additive. That is, f(x + y) = f(x) + f | StudyHelpMe
Let f : R → R be additive. That is, f(x + y) = f(x) + f(y) for all x, y ∈ R.
In addition, assume there are M > 0 and a > 0 such that if x ∈ [−a, a], then |f(x)| ≤ M.
Prove that f is uniformly continuous. In particular, prove that there is a real number m such that f(x) = mx for all x ∈ R.
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