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Suppose E is a given set, and On, for n ∈ N, is the set defined...

Suppose E is a given set, and On, for n ∈ N, is the set defined by

On = {x ∈ Rd : d(x, E) < 1/n }.

Prove that On is open and bounded then, m(E) = limn →∞ m(On).

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