Let the discussion commence!


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http://en.wikipedia.org/wiki/File:Girsanov.png

Proof

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Let (Ak) be a sequence of events in some probability space and suppose that the sum of the probabilities of the Ak is finite. That is suppose:

 

Note that the convergence of this sum implies:

 

Therefore it follows that:

 

where the abbreviation "i.o." denotes "infinitely often."