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Sequences and Subsets

1) Find a sequence {E } (n =1 to infinity) of measurable sets with E E .......... Such that ( E ) E )
2) If E is measurable subset of R Prove that given > 0, there exists an open set U E and a closed set F E such that U E) < and E F) < .
3) If E ,E are measurable subsets of [0,1], and if ( E )= 0 prove that ( E E ) = ( E )
4) Prove that a subset E of R is Measurable if and only if (E T ) = (T) for every subset T of R

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Solution Summary

Sequences and Subsets are investigated. The solution is detailed and well presented.