# Conditional Expectation Bounded

• November 16th 2011, 09:26 AM
LHeiner
Conditional Expectation Bounded
Can you help me on this proof. It is stated everywhere to show that the conditional expectation is uniform integrable. But the specific lemma is shown nowhere and I tried to proof it ( and failed (Worried))

Suppose we have a measeure space $(\Omega, \mathbb{A}, \mathbb{P})$ and $\xi\in L^1$.

$\forall \epsilon>0 \exists \delta>0$: $A\in \mathbb{A}, \mathbb{P}(A)<\delta \ \Rightarrow \int_A \left |\xi\right |d\mathbb{P}<\epsilon$.

I found that this follows with Borel Cantelli and Fatou, but how?

Thx
• November 18th 2011, 10:48 AM
LHeiner
Re: Conditional Expectation Bounded
okey, I solved it by myself!
thx anyway