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Pr(A) := lim n→∞ |An [1, n]| n exists and Pr(A) = {0, 1] that that F is an algebra (which is to say it satisfies all but the last axiom of o-

Pr(A) := lim n→∞ |An [1, n]| n exists and Pr(A) = {0, 1] that that F is an algebra (which is to say it satisfies all but the last axiom of o-

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.1: The Geometry And Algebra Of Vectors
Problem 24EQ
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Suppose that = N = { 1, 2, 3, 4, ...} and is the set of A E 2º for which |An [1, n]| n Pr(A) := lim n→∞ 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).
Transcribed Image Text:Suppose that = N = { 1, 2, 3, 4, ...} and is the set of A E 2º for which |An [1, n]| n Pr(A) := lim n→∞ 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).
Transcribed Image Text: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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