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July 15th, 2014, 07:51 AM   #1
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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.
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