Added localisable order completeness.

src/measure/vector/rn-draft.tex

@@ -50,7 +50,7 @@
     &= \sup_{A \in \cf}\braks{\int_{A \cap E}f_A d\mu + \nu_s^A(A \cap E)}
     \end{align*}
 
-    As $\cf$ is an ideal, for any $A, B \in \cf$, $A \cup B \in \cf$, and
+    By (S3), for any $A, B \in \cf$, $A \cup B \in \cf$, and
     \begin{align*}
         \int_{A \cap E}f_A d\mu \vee \int_{B \cap E}f_B d\mu &\le \int_{(A \cup B) \cap E}f_{A \cup B} d\mu \\
         \nu_s^A(A \cap E) \vee \nu_s^B(B \cap E) &\le \nu_s^{A \cup B}((A \cup B) \cap E)