Finish the proof of Theorem 18.12 (i) and show that every set (A subset mathbb{R}^{n}) is indeed

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Finish the proof of Theorem 18.12 (i) and show that every set \(A \subset \mathbb{R}^{n}\) is indeed \(\overline{\mathcal{H}}^{0}\)-measurable.

Data from theorem 18.12

Theorem 18.12 Let Hs, s20 be Hausdorff measure on (R", B(R")). (i) H is the counting measure on P(R"). (ii) H

It is a simple exercise to show that (R") are indeed the H-measurable sets. [] (ii) By Theorem 18.7 (R) C*.

(iv) We know for any E-cover (Si)iEN of A and t>s> 0 that (diam S;)

Moreover, f(4) Cf(U; Si) CU,f(Si), so (f(Si)); is an Le-cover of f(A). Therefore He(f(A))

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