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Respected members: I am trying to learn this example but I am stuck that "WHYthe sum on the right-hand side of the equation above is either 0 or ∞, which

contradicts (iii)."

Can anyone give me an example that when will it 0 and when it will ∞ ?

if I =[0, 1)

lets say that we have three sets A_0 = {0}, A_0.5 = {0.5}. A_1 = {1}

then P(0)=1/3, P(0.5)=1/3, P(1)=1/3

because after all they are just three sets and we are after the probability of A_α

therefore P([0, 1)) = ƩP(A_α) = P(0) + P(0.5) +P(1) = 1/3 + 1/3 + 1/3 = 1 and that satisfies condition that P([0, 1)) = 1

Please correct me if my approach is wrong.

Thanks in advance.

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# Uncountable additivity (sigma algebra)

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