Prove the following which we shall need later: if is a UI family of random variables such that then X ∈ L1 (and thus by Exercise 3.20). A proof of these standard results can be found in Rogers and...

Prove the following which we shall need later: if

is a UI family of random variables such that

then X ∈ L1 (and thus

by Exercise 3.20).

A proof of these standard results can be found in Rogers and Williams (1994).