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Let (0, , P) be a probability space and let F and & be two sub-o- algebras of . Suppose that they are independent, and

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Let (0, , P) be a probability space and let F and & be two sub-o- algebras of . Suppose that they are independent, and suppose that X is real valued random variable on ? which is measurable with respect to both F and . Show that X is a.s. constant; that is there is real number c E R so that P(X = c) = 1

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