diff --git a/src/measure/measurable-maps/in-measure.tex b/src/measure/measurable-maps/in-measure.tex index 5dafcf5..df9f96a 100644 --- a/src/measure/measurable-maps/in-measure.tex +++ b/src/measure/measurable-maps/in-measure.tex @@ -36,7 +36,7 @@ \begin{proposition}[{{\cite[Theorem 2.30]{Folland}}}] \label{proposition:cauchy-in-measure-limit} - Let $(X, \cm, \mu)$ be a measure space, $(Y, d)$ be a complete metric space, and $\seq{f_n}$ be Borel measurable functions from $X \to Y$, then: + Let $(X, \cm, \mu)$ be a measure space, $(Y, d)$ be a complete metric space, and $\seq{f_n} \subset Y^X$ be a sequence Borel measurable functions from $X \to Y$ that is Cauchy in measure, then: \begin{enumerate} \item There exists a Borel measurable function $f: X \to Y$ such that $f_n \to f$ in measure. \item There exists a subsequence $\seq{n_k}$ such that $f_{n_k} \to f$ almost everywhere.