format updates

content/Math4121/Math4121_L29.md

@@ -34,7 +34,8 @@ Towards proving $\mathfrak{M}$ is closed under countable unions:
 
 Any finite union/intersection of Lebesgue measurable sets is Lebesgue measurable.
 
-Proof:
+<details>
+<summary>Proof</summary>
 
 Suppose $S_1, S_2$ is a measurable, and we need to show that $S_1\cup S_2$ is measurable. Given $X$, need to show that
 
@@ -61,13 +62,14 @@ $$
 
 by measurability of $S_1$ again.
 
-QED
+</details>
 
 #### Theorem 5.10 (Countable union/intersection of Lebesgue measurable sets is Lebesgue measurable)
 
 Any countable union/intersection of Lebesgue measurable sets is Lebesgue measurable.
 
-Proof:
+<details>
+<summary>Proof</summary>
 
 Let $\{S_j\}_{j=1}^{\infty}\subset\mathfrak{M}$. Definte $T_j=\bigcup_{k=1}^{j}S_k$ such that $T_{j-1}\subset T_j$ for all $j$.
 
@@ -109,7 +111,7 @@ Therefore, $m_e(X\cap S)=m_e(X)$.
 
 Therefore, $S$ is measurable.
 
-QED
+</details>
 
 #### Corollary from the proof