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5 points let be a random variable whose values belong

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Unformatted text preview: uence of σalgebras, ℱ ⊂ ℱ a. (5 points) Let be a random variable whose values belong to . Prove that is a sequence of integrable random variables, i.e. ℱ |∞ and | b. (7 points) Let τ be a stopping time with respect to ℱ . Prove that the following holds: , ) ℱ( ℱ c. (6 points) Assume that ℱ is adapted. Let be a monotone increasing sequence of stopping-times with respect to ℱ so that ∞, a.s. Use part b to show that if ℱ is a supermartingale for each n, then ℱ is a supermartingale as well....
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