# Example of a SEQUENCE of integrable functions that converges point wise to a non-inte

1. Feb 9, 2009

### 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
??

2. Feb 10, 2009

### mathman

Re: Example of a SEQUENCE of integrable functions that converges point wise to a non-

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

3. Feb 11, 2009

### adriank

Re: Example of a SEQUENCE of integrable functions that converges point wise to a non-

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

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