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E10

[1JN] Prerequisites:[1HR], [1J3] subpoint [6].Difficulty:*.

If \(f_ n,f:I→ℝ\) are uniformly continuous on a set \(I⊂ℝ\), and \(f_ n→_ nf\) uniformly on \(I\), then \(f\) is uniformly continuous, and the family \((f_ n)_ n\) is equicontinuous.

Solution 1

[1JP]

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Authors: "Mennucci , Andrea C. G." .
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  • convergence, uniform ---
  • convergence, pointwise ---
  • function, uniformly continuous ---
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