update

pages/Math4121/Math4121_L28.md

@@ -118,3 +118,14 @@ So $S$ is measurable.
 
 QED
 
+#### Proposition 5.9 (Preview)
+
+Any finite union (and intersection) of measurable sets is measurable.
+
+Proof:
+
+Let $S_1, S_2$ be measurable sets.
+
+We prove by verifying the Caratheodory's criteria for $S_1\cup S_2$.
+
+QED