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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


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    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.
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