Whoops, didn't read one of the conditions. I will think about this more.
Hallo!
Can anybody please help me?
Is the following equality true?
is a random variable
is a sequence of random variables,
with
where denotes convergence in probability
Now, I think it follows with Fatou's Lemma for non-negative random variables, that
.
Can I now say, that
is true?
Thanks in advance!
Okay, this question is starting to make me quite nervous. The first inequality I posted should come from the fact that and the second inequality is the version of Fatou's Lemma I was able to find that concerned convergence in probability - that is, provided we have convergence in probability, i.e. you can get rid of the liminf.