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19. Completion. Let (2, B, P) be a probability space. Call a set N null if = 0. Call a set BC2 negligible if there exists a null set N such that BCN. Notice that for B to be negligible, it is not required that B be measurable. Denote the set of all negligible subsets by N. Call B complete (with respect to P) if every negligible set is null. What if B is not complete? Define B* := {AUM : A e B, M e N}. (a) Show B* is a o-field.

19. Completion. Let (2, B, P) be a probability space. Call a set N null if = 0. Call a set BC2 negligible if there exists a null set N such that BCN. Notice that for B to be negligible, it is not required that B be measurable. Denote the set of all negligible subsets by N. Call B complete (with respect to P) if every negligible set is null. What if B is not complete? Define B* := {AUM : A e B, M e N}. (a) Show B* is a o-field.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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19. Completion. Let (2, B, P) be a probability space. Call a set N null if N e B and P(N) = 0. Call a set B C2 negligible if there exists a null set N such that BCN. Notice that for B to be negligible, it is not required that B be measurable. Denote the set of all negligible subsets by N. Call B complete (with respect to P) if every negligible set is null. What if B is not complete? Define B* := {AUM : A e B, M E N). (a) Show B* is a o-field.
Transcribed Image Text:19. Completion. Let (2, B, P) be a probability space. Call a set N null if N e B and P(N) = 0. Call a set B C2 negligible if there exists a null set N such that BCN. Notice that for B to be negligible, it is not required that B be measurable. Denote the set of all negligible subsets by N. Call B complete (with respect to P) if every negligible set is null. What if B is not complete? Define B* := {AUM : A e B, M E N). (a) Show B* is a o-field.
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