Question: Take ( = (, and let An be the -field generated by the class {(0, 1), [1, 2),..., [n - 1, n)]}, n 1.

Take ( = (, and let An be the σ-field generated by the class {(0, 1), [1, 2),..., [n - 1, n)]}, n ≥ 1. Then show that
(i) An ( An+1, n ≥ 1, and indeed An ( An+1, n ≥ 1.
(ii) The class ∪∞n=1 An, is not a σ-field.
(iii) Describe explicitly A1 and A2.

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i We have 0 1 1 2 n1 n 0 1 1 2 n1 n n n1 and hence A n A n1 That A n A n1 follows by the f... View full answer

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