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3. Let B = (Bt) TER + a standard Brownian motion on a probability space (2, A, P) and M = max tejo.1] | B t | their maximum amount up to time 1. (a) (3 points) Prove that M is a random variable on (2, A, P), i.e. that it is A-measurable. (b) (6 points) Prove ME Lp (2, A, P) for all p E R with p> 1