HW08.pdf - Modern Analysis 2 Homework 08 1 Let be a measure...

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Modern Analysis 2 Homework 08 1. Let μ be a measure on the σ -algebra A on Ω; let ( A n ) n =0 be a sequence of sets in A such that n =0 μ ( A n ) < . Prove that almost every ω in Ω lies in A n for only finitely many values of n . [Notice that { ω Ω : ω A n for infinitely many n } is related to either lim inf n A n or lim sup n A n ; which and how?]
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