Register to reply

Uniform convergence of piecewise continuous functions

Share this thread:
Nov13-10, 01:43 PM
Demon117's Avatar
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?
Phys.Org News Partner Science news on
Apple to unveil 'iWatch' on September 9
NASA deep-space rocket, SLS, to launch in 2018
Study examines 13,000-year-old nanodiamonds from multiple locations across three continents

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