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Math Help - Conditional Expectation Bounded

  1. #1
    Junior Member
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    Oct 2010
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    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 )

    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
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  2. #2
    Junior Member
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    Oct 2010
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    Re: Conditional Expectation Bounded

    okey, I solved it by myself!
    thx anyway
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