a) Let A1, A2,..., An be a finite collection of subsets of N such that A;...

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a) Let A1, A2,..., An be a finite collection of subsets of N such that A; € Fo (an algebra), 1<i< n. Show that U A; E Fo and N A; E Fo. Hence, infer that an algebra is closed under finite union n 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 N such that A; € Fo (an algebra), 1<i< n. Show that U A; E Fo and N A; E Fo. Hence, infer that an algebra is closed under finite union n 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

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A A be a collection of subsets of such that each AFo ... View the full answer