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content/Math4121/Math4121_L25.md

@@ -48,7 +48,8 @@ The Borel sets are Borel measurable.
 
 (proof in the following lectures)
 
-Examples:
+<details>
+<summary>Examples for Borel measurable</summary>
 
 1. Let $S=\{x\in [0,1]: x\in \mathbb{Q}\}$
 
@@ -62,6 +63,8 @@ Since $c_e(SVC(4))=\frac{1}{2}$ and $c_i(SVC(4))=0$, it is not Jordan measurable
 
 $S$ is Borel measurable with $m(S)=\frac{1}{2}$. (use setminus and union to show)
 
+</details>
+
 #### Proposition 5.3
 
 Let $\mathcal{B}$ be the Borel sets in $\mathbb{R}$. Then the cardinality of $\mathcal{B}$ is $2^{\aleph_0}=\mathfrak{c}$. But the cardinality of the set of Jordan measurable sets is $2^{\mathfrak{c}}$.