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Set Measures and Measurability

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9. Let F be a closed subset in R, and ... the distance from x to F, that is,
.......
Clearly, ....) whenever .... Prove the more refined estimate .... for a.e. xEF,
that is,.....
[Hint: Assume that x is a point of density of F.]

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Set measures and measurability are investigated in the solution.

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