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made fact from lecture 13 (somewhat) less trivial

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Josia Pietsch 2023-07-15 23:31:10 +02:00
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inputs/lecture_13.tex
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@ -274,7 +274,8 @@ We have shown, that $\mu_{n_k} \implies \mu$ along a subsequence.
We still need to show that $\mu_n \implies \mu$. We still need to show that $\mu_n \implies \mu$.
\begin{fact} \begin{fact}
Suppose $a_n$ is a bounded sequence in $\R$, Suppose $a_n$ is a bounded sequence in $\R$,
such that any subsequence converges to $a \in \R$. such that any subsequence has a subsequence
that converges to $a \in \R$.
Then $a_n \to a$. Then $a_n \to a$.
\end{fact} \end{fact}
\begin{subproof} \begin{subproof}