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Zheyuan Wu
2025-03-24 10:54:32 -05:00
parent da7b8f58a6
commit 6805462262
3 changed files with 95 additions and 5 deletions

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@@ -2,7 +2,7 @@
## Continue on Measure Theory
### Borel Mesure
### Borel Measure
Finite additivity of Jordan content, i.e. for any $\{S_j\}_{j=1}^N$ pairwise disjoint sets and Jordan measurable, then
@@ -73,5 +73,3 @@ SVC(3) is Jordan measurable, but $|SVC(3)|=\mathfrak{c}$. so $|\mathscr{P}(SVC(3
But for any $S\subset \mathscr{P}(SVC(3))$, $c_e(S)\leq c_e(SVC(3))=0$ so $S$ is Jordan measurable.
However, there are $\mathfrak{c}$ many intervals and $\mathcal{B}$ is generated by countable operations from intervals.