 Stating it for two events implies the equality only for finitely many events finite additivity not for countably many countable additivity It is in fact possible to reject countable additivity and get a different kind of probability theory but its not common   

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 Stating it for two events implies the equality only for finitely many events finite additivity not for countably many countable additivity It is in fact possible to reject countable additivity and get a different kind of probability theory but its not common   

