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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.