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Lp Spaces and Convergence

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Please see the attached.
You can help with either part a or b. If you can help with one of them then I will try to figure out the other.
Also there is a typo on part a: Convergence of the sequence of random variables should not be in probability it is convergence almost surely. So on the top of the arrow of the given convergence should be a.s instead of P.

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The solution discusses Lp spaces and convergence

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