1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Uniform convergence

  1. May 4, 2006 #1
    I'm studying for finals and I just need some feedback.
    One of questions MIGHT be:
    If I know a sequence of functions is pointwise convergent, how do I show that it's not uniformly convergent?
    I think that a pointwise convergent sequence of functions might not converge to a continuous function, although it might.
    Also, you can't interchange the limit and the derivitive, or the limit and the integral.
    Am I right? Am I missing something?
    Any feedback will be appreciated.
  2. jcsd
  3. May 4, 2006 #2


    User Avatar
    Science Advisor
    Homework Helper

    Find a counterexample. A standard example involves growing steeples, i.e. the nth function is 0 everywhere except on [2n,2n+2], say, and on this interval, it is basically an isoceles triangle with its value at 2n and 2n+2 being 0, and its value at 2n+1 being n, say.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook