Suppose that 2 = N = {1, 2, 3, 4, ...) and F is the set of A 22 for which |An [1, n]| n Pr(A) := lim 818 exists and Pr(A) = {0, 1}. Show that that F is an algebra (which is to say it satisfies all but the last axiom of o-algebras). Show by example that in the previous problem F is not a o--algebra and Pr is not continuous at (the 4- th axiom of probability).