Give an example of a uniformly integrable martingale which is not in H^1.
(a martingale (X_t) is H^1 if EX^* is finite, where X^*(w) = \sum_t |X_t|)
See ex 3.15 on page 74 of the following book for some hints. This result is
not intuitive, (therefore interesting). I don't know how to construct such
an example. http://books.google.com/books?id=1ml95FLM5koC&lpg=PP1&dq=Revuz%20Yor&pg=PA74#v=onepage&q=&f=false
