Prove the assertions made in Example 3.3 (iv), (vi) and (vii). [ use (2.6) for (vii).] Data

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Prove the assertions made in Example 3.3 (iv), (vi) and (vii). [ use (2.6) for (vii).]

Data from example 3.3

(i) P(X) is a o-algebra (the maximal o-algebra in X). (ii) {0, X) is a o-algebra (the minimal o-algebra in

(v) A={ACX: #A < #Nor #A < #N] is a o-algebra. Proof: Let us verify () (3). (): X = 0), which is certainly

Equation 2.6

(Uci)=U^(C), iEI iEI f'(na)=(C), iEI iEI f(C\D)=f(C) \(D).

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