a) Let A1, A2,..., An be a finite collection of subsets of 2 such that Ai...

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a) Let A1, A2,..., An be a finite collection of subsets of 2 such that Ai € Fo (an algebra), 1<i< n. Show that U A, E Fo and n A, € Fo. Hence, infer that an algebra is closed under finite union i=1 i=1 and finite intersection. b) Suppose A1, A2, A3, . is a countable collection of subsets in the o-algebra F, then show that N A, E F. i=1 a) Let A1, A2,..., An be a finite collection of subsets of 2 such that Ai € Fo (an algebra), 1<i< n. Show that U A, E Fo and n A, € Fo. Hence, infer that an algebra is closed under finite union i=1 i=1 and finite intersection. b) Suppose A1, A2, A3, . is a countable collection of subsets in the o-algebra F, then show that N A, E F. i=1