Examples of Pointwise Convergence of Integrable Functions to Non-Integrable

[irresistible]

hey guys,
Any one can think of any examples ?
Of a sequence of integrable functions{fn} on [0,1] that converges pointwise to a non-integrable function f:[0,1] --> R
??

 

[mathman]

fn=1/x for x>1/n, fn=n for x<1/n.

 

[adriank]

mathman, I don't believe that function converges pointwise (specifically at 0). Setting f_n(0) = 0 will fix that, though.