(Solution Library) Given δ>0, show that m^*(E)= ∈ f ∑_n=1^∞ \ell(I_n) where the infimum is taken over all coverings of E by sequences of intervals
Question: Given \(\delta>0\), show that \(m^{*}(E)=\inf \sum_{n=1}^{\infty} \ell\left(I_{n}\right)\) where the infimum is taken over all coverings of \(E\) by sequences of intervals \(\left(I_{n}\right)\), where each \(I_{n}\) has diameter less than \(\delta\).
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