format updates

This commit is contained in:
Zheyuan Wu
2025-09-24 01:27:46 -05:00
parent e59ef423f3
commit 143d77e7f9
16 changed files with 401 additions and 79 deletions

View File

@@ -110,7 +110,8 @@ $$
So $S$ is Jordan measurable if and only if $c_e(\partial S)=0$.
Proof:
<details>
<summary>Proof</summary>
Let $\epsilon > 0$, and $\{R_j\}_{j=1}^N$ be an open cover of $\partial S$. such that $\sum_{j=1}^N \text{vol}(R_j) < c_e(\partial S)+\frac{\epsilon}{2}$.
@@ -136,4 +137,4 @@ If $\eta$ is small enough (depends on $\delta$), then $\mathcal{C}_\eta=\{Q\in K
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.)
EOP
</details>