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Math Help - convergence in Lp space

  1. #1
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    convergence in Lp space

    Let (g_n) be a sequence that does not convergence in L_p to a function f\in L_p and let (h_n) be a subsequence of (g_n) that convergence in L_p to f.
    Does any contradiction exists?
    I know if it is the case where convergence is in \mathbb{R},it is trivially true.But,what about in L_p?
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  2. #2
    Super Member Rebesques's Avatar
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    Also (trivially) true, consider \{g_1,f,g_2,f,\ldots\}
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