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Probability : Finitely Additive / Countably Additive

Please use words to describe the solution process. (I've attached a possibly useful review of probability).

Suppose that P is finitely additive on an alegbra {field} A. Show that P is countably additive on A <---> whenever {An} is a sequence in ... *see attachment*


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The concepts Finitely Additive and Countably Additive are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who posted the question.