Let be a sequence of random variables on a probability space such that a.e. Show that if , then .
I will try to explain as best I can. First, I have a version of Fatou's Lemma stating that if is a sequence of non-negative random variables, then .
If we let then I have a sequence of non-negative random variables to work with. One concern of mine is this: can I assume that ? I feel like that's necessary for for what I've written below to work.
If I can make that assumption then we have