4 Prove Borel Cantelli theorem (lecture notes p.16) i.e. Let (2, F, P) be a probability space and let {E₁} be a sequence of events. 1. If P(E) ≤ ∞ then P(lim sup En) = 0 Σ. 1 2. If {E} is a sequence of independent events then P(lim sup En) = 0 or 1 provided that the series P(E₁) converges or diverges. V1

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