HW207 - It follows that if ∑ ∞ n =1 μ A n< ∞ then...

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Modern Analysis 2 Homework 07 1. Let ( A n ) n =1 be a sequence in M . For m a positive integer, let B m be the set comprising all elements that lie in A n for at least m values of n . Prove that B m ∈ M and m μ ( B m ) 6 X n =1 μ ( A n ) . Remark
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Unformatted text preview: : It follows that if ∑ ∞ n =1 μ ( A n ) < ∞ then the set B ∞ = { x : x ∈ A n i . o . } is null; this is the ‘first Borel-Cantelli lemma’. 1...
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