Uniform convergence of piecewise continuous functions


by Demon117
Tags: continuous, convergence, functions, piecewise, uniform
Demon117
Demon117 is offline
#1
Nov13-10, 01:43 PM
Demon117's Avatar
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?
Phys.Org News Partner Science news on Phys.org
Better thermal-imaging lens from waste sulfur
Hackathon team's GoogolPlex gives Siri extra powers
Bright points in Sun's atmosphere mark patterns deep in its interior

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