(Solution) - Let A P 0 1 B 0 1 -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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Let ((, A, P) = ((0, 1), B(0, 1), (), where ( is the Lebesgue measure, and let Xn be a r.v. defined by

Let ((, A, P) = ((0, 1), B(0, 1), (),
Then show that
Let ((, A, P) = ((0, 1), B(0, 1), (),
For any r > 0, and
Let ((, A, P) = ((0, 1), B(0, 1), (),
Indeed,
Let ((, A, P) = ((0, 1), B(0, 1), (),
Pointwise.