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    Probability : Finitely Additive / Countably Additive

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    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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    A. We will use the following axioms (hypotheses):
    1) P is finitely additive:
    ( 1)
    2) ( 2)
    and we will prove that
    or ( 3)

    If that means that ( 4)
    Since , we can write:
    ( 5)
    because like (Ai) ...

    Solution Summary

    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.