Replaced mentions of normed spaces to normed vector spaces.
All checks were successful
Compile Project / Compile (push) Successful in 17s
All checks were successful
Compile Project / Compile (push) Successful in 17s
This commit is contained in:
@@ -125,7 +125,7 @@
|
||||
|
||||
\begin{proposition}
|
||||
\label{proposition:measurable-simple-separable-norm}
|
||||
Let $(X, \cm)$ be a measurable space, $(E, \norm{\cdot}_E)$ be a separable normed space, and $f: X \to E$, then the following are equivalent:
|
||||
Let $(X, \cm)$ be a measurable space, $(E, \norm{\cdot}_E)$ be a separable normed vector space, and $f: X \to E$, then the following are equivalent:
|
||||
\begin{enumerate}
|
||||
\item $f$ is $(\cm, \cb_E)$-measurable.
|
||||
\item There exists simple functions $\seq{f_n}$ such that $\abs{f_n} \le \abs{f}$ for all $n \in \natp$, and $f_n \to f$ pointwise.
|
||||
|
||||
Reference in New Issue
Block a user