Author Topic: Pointwise convergence  (Read 1566 times)

Sang-drax

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Pointwise convergence
« on: September 21, 2005, 03:12:07 PM »
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.