Prove Borel Cantelli theorem (lecture notes p.16 ) i.e. Let (2, F, P) be a probability space and let {E} be a sequence of events. 1. If Σ P(E) ≤ [infinity] then P(lim sup E₁) = 0 2. If {E} is a sequence of independent events then P(lim sup E₁) = 0 or 1 provided that the series P(E₁) converges or diverges. (30 pts)