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@@ -14,7 +14,8 @@ $$
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where $\partial S$ is the boundary of $S$ and $c_e(\partial S)=0$.
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Example:
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<details>
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<summary>Examples for Jordan measurable</summary>
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1. $S=\mathbb{Q}\cap [0,1]$ is not Jordan measurable.
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@@ -56,6 +57,8 @@ So $c_e(SVC(4))=\frac{1}{2}$.
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> General formula for $c_e(SVC(n))=\frac{n-3}{n-2}$, and since $SVC(n)$ is nowhere dense, $c_i(SVC(n))=0$.
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</details>
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### Additivity of Content
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Recall that outer content is sub-additive. Let $S,T\subseteq \mathbb{R}^n$ be disjoint.
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@@ -80,7 +83,8 @@ $$
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c(\bigcup_{i=1}^N S_i)=\sum_{i=1}^N c(S_i)
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$$
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Proof:
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<details>
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<summary>Proof</summary>
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$$
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\begin{aligned}
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@@ -96,7 +100,7 @@ $$
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c(\bigcup_{i=1}^N S_i)=\sum_{i=1}^N c(S_i)
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$$
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QED
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</details>
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##### Failure for countable additivity for Jordan content
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