July 15th, 2014, 07:51 AM  #1 
Newbie Joined: Jun 2014 From: Canada Posts: 3 Thanks: 0  Reverse Fatou Lemma
Let $(\Omega, \mathcal{F}, \mathbb{P})$ be probability space and ${E}_{n} \in \mathbb{N}$ be $\mathcal{F}$measurable sets. Show example that reverse Fatou's Lemma, $\mathbb{P}(\limsup_n E_n)\geq \limsup_n \mathbb{P}(E_n)$, meets inequality strictly. I understand this inequality of inf. However, I cannot solve this. 

Tags 
fatou, lebesgue, lemma, measure theory, reverse 
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