EntropySink
Nothing & Everything => Open Discussion => Topic started by: Sang-drax on September 21, 2005, 03:12:07 PM
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If a function series converges pointwise to a continuous function f(x), isn't it automatically uniformly convergent?
I can see how it doesn't have to be uniform when f(x) isn't continuous.
For example, fn(x) = x^n will converge to a function f(x) that is equal to 0 when x<1 and equal to 1 when x=1. The convergence isn't uniform, but f(x) isn't continuous.