@Tom Boardman: Doesn't fatou's lemma deal with this type of integral. The final statement of Fatou's lemma is $$\int\limts_{E} f \ dm \leq \lim_{n} \inf \int\limits_{E} f_{n} \ dm$$ Also, whats wrong in thinking that way. Its my think. I did think something about characteristic function, but didn't work. — anonymous Aug 10 '10 at 15:21