From bc9927a32608753cceaaf86121d43b0db3c8910f Mon Sep 17 00:00:00 2001
From: Bokuan Li <bokuan.li@mail.mcgill.ca>
Date: Wed, 21 Jan 2026 10:31:25 -0500
Subject: [PATCH] Enforced Borel sigma algebra convention.

---
 src/measure/measure/index.tex      | 1 +
 src/measure/measure/kolmogorov.tex | 2 +-
 src/measure/measure/radon.tex      | 2 +-
 src/measure/measure/riesz.tex      | 2 ++
 4 files changed, 5 insertions(+), 2 deletions(-)
 create mode 100644 src/measure/measure/riesz.tex

diff --git a/src/measure/measure/index.tex b/src/measure/measure/index.tex
index b91ccf3..de6fd69 100644
--- a/src/measure/measure/index.tex
+++ b/src/measure/measure/index.tex
@@ -9,4 +9,5 @@
 \input{./src/measure/measure/radon.tex}
 \input{./src/measure/measure/outer.tex}
 \input{./src/measure/measure/lebesgue-stieltjes.tex}
+\input{./src/measure/measure/radon.tex}
 \input{./src/measure/measure/kolmogorov.tex}
diff --git a/src/measure/measure/kolmogorov.tex b/src/measure/measure/kolmogorov.tex
index e613e86..9931b49 100644
--- a/src/measure/measure/kolmogorov.tex
+++ b/src/measure/measure/kolmogorov.tex
@@ -19,7 +19,7 @@
     \end{enumerate}
     Let $\bracs{\mu_{I}| I \subset \natp \text{ finite}}$ be consistent Borel probability measures, then for any $\seq{B_n}$ where:
     \begin{enumerate}
-        \item[(d)] For each $n \in \nat$, $B_n \in \cb(\prod_{j = 1}^n X_j)$.
+        \item[(d)] For each $n \in \nat$, $B_n \in \cb_{\prod_{j = 1}^n X_j}$.
         \item[(e)] For each $n \in \nat$, $B_{n+1} \subset B_n \times X_{n+1}$.
         \item[(f)] There exists $\eps > 0$ such that $\mu_{[n]}(B_n) > \eps$ for all $n \in \natp$.
     \end{enumerate}
diff --git a/src/measure/measure/radon.tex b/src/measure/measure/radon.tex
index d467060..8a9b76c 100644
--- a/src/measure/measure/radon.tex
+++ b/src/measure/measure/radon.tex
@@ -3,7 +3,7 @@
 
 \begin{definition}[Radon Measure]
 \label{definition:radon-measure}
-    Let $X$ be a LCH space and $\mu: \cb(X) \to [0, \infty]$ be a Borel measure, then $\mu$ is a \textbf{Radon measure} if:
+    Let $X$ be a LCH space and $\mu: \cb_X \to [0, \infty]$ be a Borel measure, then $\mu$ is a \textbf{Radon measure} if:
     \begin{enumerate}
         \item For any $K \subset X$ compact, $\mu(K) < \infty$.
         \item $\mu$ is outer regular on all Borel sets.
diff --git a/src/measure/measure/riesz.tex b/src/measure/measure/riesz.tex
new file mode 100644
index 0000000..4099aea
--- /dev/null
+++ b/src/measure/measure/riesz.tex
@@ -0,0 +1,2 @@
+\section{Riesz Representation Theorem}
+\label{section:riesz-radon}