Show that lim, P(lim inf, A4) = 0. Hunt: Show that lim sup lim inf A...

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Show that lim, P(lim inf, A4) = 0. Hunt: Show that lim sup lim inf A A% is empty. k Put A* - lim sup, A, and A, = lim inf, An (b) Show that P(A, -A*)-0 and P(A, -A)-0. (c) Show that A, →A (in the sense that A = A* = A₂) implies P(AAA) -0. (d) Suppose that A, converges to A in the weaker sense that P(AAA*)= P(AAA) 0 (which implies that P(A* - A,)=0). Show that P(AAA) -0 (which implies that P(A)→ P(A)). Show that lim, P(lim inf, A4) = 0. Hunt: Show that lim sup lim inf A A% is empty. k Put A* - lim sup, A, and A, = lim inf, An (b) Show that P(A, -A*)-0 and P(A, -A)-0. (c) Show that A, →A (in the sense that A = A* = A₂) implies P(AAA) -0. (d) Suppose that A, converges to A in the weaker sense that P(AAA*)= P(AAA) 0 (which implies that P(A* - A,)=0). Show that P(AAA) -0 (which implies that P(A)→ P(A)).

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a To show that lim suplim infk A n cap A k c is emptywe can use the following steps LetSkliminfkAnAk... View the full answer