Question: Establish the following generalized (Dominated Convergence Theorem). Namely, for n = 1, 2, ...., let Xn, Un, X, U be r.v.s such that finite. Then,

Establish the following generalized (Dominated Convergence Theorem). Namely, for n = 1, 2, ...., let Xn, Un, X, U be r.v.s such that finite. Then, as n→(:
(i) ( Xn → X finite; (ii) ( |Xn - X| → 0; (iii) (A Xn → (A X uniformly in A( A.

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