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Apr 26, 2024 at 20:41 comment added Maxxer Uniform convergence on an interval means that this sequence is uniformly convergent on (a, b) because it can be non-uniformly convergent or even divergent outside of this interval. Because the domain is an (a, b) interval think of it as normal uniform convergence. Just remember to put $x∈(a,b)$ everywhere needed in your proof.
Apr 26, 2024 at 20:27 history edited Jose Avilez CC BY-SA 4.0
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S Apr 26, 2024 at 20:11 vote accept rudinable
S Apr 26, 2024 at 20:11 vote accept rudinable
S Apr 26, 2024 at 20:11
Apr 26, 2024 at 20:11 vote accept rudinable
S Apr 26, 2024 at 20:11
Apr 26, 2024 at 18:36 comment added GEdgar It is not the function $f$ that is uniformly convergent. The series $\sum_{n=1}^\infty f_n$ is uniformly convergent. It is perhaps confusing (but nevertheless common) to use the same letter for the series and for the sum of the series.
Apr 26, 2024 at 18:34 answer added Mousedorff timeline score: 1
Apr 26, 2024 at 18:27 answer added Jose Avilez timeline score: 1
Apr 26, 2024 at 18:27 comment added Mason $g$ is uniformly convergence means the partial sums are uniformly convergent (to $g$).
Apr 26, 2024 at 18:24 history asked rudinable CC BY-SA 4.0