Suppose that 2 = N = {1, 2, 3, 4, ...) and F is the set...

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Suppose that 2 = N = {1, 2, 3, 4, ...) and F is the set of A € 2º2 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 Ø (the 4- th axiom of probability). Suppose that 2 = N = {1, 2, 3, 4, ...) and F is the set of A € 2º2 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 Ø (the 4- th axiom of probability).

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13 Solution Glven 1 2 3 4 A Postion of x pr A lim is a An LT Pola 01 M Collocation of dis j... View the full answer