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Thread: Pointwise convergence

  1. April 9th 2010, 11:41 AM #1
    Chandru1
    Chandru1 is offline
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    Pointwise convergence

    Let E=[0,\infty) and f_{n}=\frac{1}{n} \chi_{[0,n]}, n =1,2,.... Show that \{f_n\} converges pointwise to the function f \equiv 0 on E, {f_n} is uniformly bounded on E but

    \int\limits_{E} f \ dx \neq \lim_{n \to \infty} \int\limits_{E} f_{n} \ dx

    Does this contradict the bounded convergence theorem.
    Last edited by Chandru1; April 9th 2010 at 11:43 AM. Reason: mistake boss!
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