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Sequences : Cantor Sets (2 Problems)

1) a. Let with . If is a measurable subset of R, prove that
and are measurable.
b. let E =[0,1]Q. Prove that E is measurable and (E)=1.
c. let P denote the cantor set in [0,1]. Prove that
2) If E R, prove that ther exists a sequence { } of open sets with E for all n such that = .

(See attached file for full problem description)


Solution Summary

Sequences, Measurable Sets and Cantor Sets are investigated. The solution is detailed and well presented.