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(b) Let P and P be two probability measures satisfying the relation P(w) = Z(w)P(w) for some random variable Z(w). Two probability measure are equivalent

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(b) Let P and P be two probability measures satisfying the relation P(w) = Z(w)P(w) for some random variable Z(w). Two probability measure are equivalent if they agree on which events have probability zero. In other words, P and P are equivalent if P(A) = 0 - P(A) = 0. Prove or disprove: if P(Z > 0) = 1, then P and P are equivalent

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