Question: 5. (a) (10 marks) Prove that A = {1: : :1: E R and x has a decimal representation 0421112113 . . . , where

5. (a) (10 marks) Prove that A = {1: : :1: E R and x has a decimal representation 0421112113 . . . , where a1, a3, a5, . . . are zeros} is a measurable set and m(A) = 0. (b) (10 marks) Prove that there exists two nonempty measurable subsets B and C of R such that m(B)=0, m(0)=0 and R={:r+y::rB,yEC}

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