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...

19. Completion. Let (2, B, P) be a probability space. Call a set N null if<br>N e B and P(N) = 0. Call a set B C2 negligible if there exists a null<br>set N such that BCN. Notice that for B to be negligible, it is not required<br>that B be measurable. Denote the set of all negligible subsets by N. Call B<br>complete (with respect to P) if every negligible set is null.<br>What if B is not complete? Define<br>B* := {AUM : A e B, M E N).<br>(a) Show B* is a o-field.<br>

Extracted 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.

Jun 11, 2022

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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...

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