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Let P be some probability measure on sample space S = [0, 1]. (a) Prove that...

Let P be some probability measure on sample space S = [0, 1]. (a) Prove that we must have limn→∞ P((0, 1/n) = 0. (b) Show by example that we might have limn→∞ P ([0, 1/n)) > 0.

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9olution: i)if A\, An are disjoinl sels subsets o PCiU Aỉ ) : Σ.PM) en lim o, o rom (T N, Suppo se, we have pm 2 3 considerlim) Henre proved Hente

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