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Borel Cantelli Lemma


Suppose \{E_k\}_{k=1}^\infty is a countable family of measurable sets of a measure space (X,\mathcal{A},m) and \displaystyle \sum_{k=1}^\infty m(E_k)< \infty.
Then if we define E=\displaystyle \bigcap_{n=1}^\infty \bigcup_{k\geq n}E_k= \limsup_{k \to \infty}E_k we have m(E)=0.

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  1. April 24, 2010 at 8:14 pm

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