Adjusted notation for spaces of measurable functions.

2026-06-22 12:55:37 -04:00
parent b52626f3a1
commit 3bf3f2a85c
2 changed files with 10 additions and 3 deletions
@@ -12,7 +12,8 @@
    $\mathcal{B}_X$ & Borel $\sigma$-algebra on $X$. & \autoref{definition:borel-sigma-algebra} \\
    $\sigma(\{f_i \mid i \in I\})$ & $\sigma$-algebra generated by the maps $\{f_i\}$. & \autoref{definition:generated-sigma-algebra-function} \\
    $\bigotimes_{i \in I} \mathcal{M}_i$ & Product $\sigma$-algebra. & \autoref{definition:product-sigma-algebra} \\
-    $\mathscr{M}(X; Y)$ & Space of measurable functions from $X$ to $Y$. & \autoref{definition:measurable-function} \\
+    $\mathcal{L}^0(X; Y)$ & Space of measurable functions from $X$ to $Y$. & \autoref{definition:measurable-function-space} \\
+    $L^0(X; Y)$ & Space of measurable functions from $X$ to $Y$, modulo almost everywhere equality. & \autoref{definition:measurable-function-space} \\
    $\chi_E = \mathbf{1}_E$ & Indicator function of $E$. & \autoref{definition:indicator-function} \\
    $\Sigma(X, \mathcal{M}; E)$ & Space of $E$-valued simple functions on $(X, \mathcal{M})$. & \autoref{definition:simple-function-standard-form} \\
    $\Sigma^+(X, \mathcal{M})$ & Space of non-negative simple functions. & \autoref{definition:simple-function-scalar} \\