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@@ -110,7 +110,8 @@ $$
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So $S$ is Jordan measurable if and only if $c_e(\partial S)=0$.
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Proof:
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<details>
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<summary>Proof</summary>
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Let $\epsilon > 0$, and $\{R_j\}_{j=1}^N$ be an open cover of $\partial S$. such that $\sum_{j=1}^N \text{vol}(R_j) < c_e(\partial S)+\frac{\epsilon}{2}$.
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@@ -136,4 +137,4 @@ If $\eta$ is small enough (depends on $\delta$), then $\mathcal{C}_\eta=\{Q\in K
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Suppose $\exists x\in S$ but not in $\mathcal{C}_\eta$. Then $x$ is closed to $\partial S$ so in some $Q_j$. (This proof is not rigorous, but you get the idea. Also not clear in book actually.)
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EOP
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</details>
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