Let $1, $2, . be a sequence of random variables on a probability space (0, F, P), and G be a o-subalgebra of F. Assume that En is independent of G...
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How to prove independency?

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3. Let $1, $2, ... be a sequence of random variables on a probability space
(0, F, P), and G be a o-subalgebra of F. Assume that En is independent of G
for each n, and that limn-+0 En = & almost surely. Prove that & is independent
of g.

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