Mean of a Distribution Question

[Epsilon36819]

Here goes:

If F is a probability distribution function and /phi is its integrable characteristic function. If the mean of F exists, why can we say that there exists u>0 st int[abs(1- /phi(t))/t] < infinity, where the integral is over the set of all t st abs(t)<u ?

(abs = absolute value)

I just. Can`t. See. It.

Thanks in advance for your help.

 

[mathman]

I'm not completely sure of details, but you would use phi(t) ~ 1 +iFt for t near 0.