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part 1

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part 2

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part 3

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Let X be a non-empty collection of o-fields on the same sample space 12. Show that the intersection Neex F of all these o-fields is also a o-field on N.

Show that Pr(U21 A;) < Liz Pr(Ai), for any arbitrary countable collection of events A1, A2 ... (not necessarily pairwise disjoint).

Give an example of a field of sets which is not a o-field