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    Probabilities and Set Theory

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    Let (Omega, A) be a measurable space, and P:A--> [0,infinity] an application such that P(AUB) = P(A) + P(B) when A,B E A and A intersection B = ø, and P(Omega) = 1 . Prove that the following statements are equivalent:
    (i) P is a probability
    (ii) P is continuous on the decreasing series:

    (iii) P is continuous on the increasing series:

    (iv) and ø

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    https://brainmass.com/math/discrete-math/probabilities-set-theory-13314

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    Let be a mesurable space, and an application such that when and ø, and . Prove that the following statements are equivalent:
    (i) P is a probability
    (ii) P is ...

    Solution Summary

    Proofs are provided for proabilities expressed with set theory. The solution is detailed and well presented.

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