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Chapter 1 Measure on a ¾Algebra of Sets 1 Limits of sequences of sets Deflnition 1 Let (An)n2Nbe a sequence of subsets of a set X (a) We say that (An) is increasing if An ‰ An1 for all n 2 N, and decreasing if An ¾ An1 for all n 2 N (b) For an increasing sequence (An), we deflne lim n!1 An= 1n=1 An For a decreasing sequence (An), we deflne lim.
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