## 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?