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real Analysis 1). Let C be the intersection of all the Cn's. You must show C is closed,...

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Advance Math

real Analysis
1).Let C be the intersection of all the Cn's. You must show C isclosed, measurable, has positive measure, and contains no interval,i.e., if x is in C, every epsilon neighborhood of x contains pointsnot in C.Analysis
i should have note 0
Start with the interval [0,1] and remove the middle openinterval of length alpha/3 to form C1. Cn is then formed byremoving the middle open interval of length alpha/3^n from eachclosed interval of C(n-1). Let C be the intersection of all theCn's. You must show C is closed, measurable, has positive measure,and contains no interval, i.e., if x is in C, every epsilonneighborhood of x contains points not in C.

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We first show that C is closed    See Answer
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