# convergence in Lp, convergence for p smaller infinity

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• October 22nd 2012, 12:39 PM
huberscher
Re: convergence in Lp, convergence for p smaller infinity
What about this example:

$f_n:=\frac{1}{n*x}$

$\forall x \in (0,\frac{1}{2}) \rightarrow |f_n(x)|\ge \frac{1}{n*\frac{1}{2*n}}=2$

and $\int_{[0,1]} |f_n|^p = \frac{1}{n^p * (1-p)}$

I think this one clearly works now, yes?
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