HW06.pdf - Modern Analysis Homework 1 Let(fn n=0 be a...

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Modern Analysis Homework 1. Let ( f n ) n =0 be a sequence of real-valued functions on the measurable space , A ). Prove that the set C , comprising all ω Ω such that the real sequence ( f n ( ω )) n =0 converges, lies in A . 2. Let (Ω , A , μ ) be a measure space. Let ( A n ) n =0 be a sequance in A that is decreasing in the sense that A n A n +1 for each n > 0. (i) Prove that if μ ( A N ) < for some N > 0 then μ ( A n ) μ
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