Uniform convergence of piecewise continuous functionsby Demon117 Tags: continuous, convergence, functions, piecewise, uniform 

#1
Nov1310, 01:43 PM

P: 162

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? 


Register to reply 
Related Discussions  
Uniform convergence of series of functions  Calculus & Beyond Homework  2  
Transforming piecewise continuous functions  Calculus  4  
Uniform Converges of Continuous Increasing Functions  Calculus & Beyond Homework  19  
Sequence of Functions Converges to Continuous Function Implies Convergence Is Uniform  Calculus & Beyond Homework  0  
Uniform convergence of integrable functions  Calculus  3 