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Uniform convergence of piecewise continuous functions 
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#1
Nov1310, 01:43 PM

P: 165

I like thinking of practical examples of things that I learn in my analysis course. I have been thinking about functions fn:[0,1] >R. What is an example of a sequence of piecewise functions fn, that converge uniformly to a function f, which is not piecewise continuous?
I've thought of letting each of these sequences of functions being piecewise in terms of the fourier series but I am unsure this really works because I haven't figured out what it would converge to. Any suggestions or other examples? 


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