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\vspace*{.3in}
\noindent{\bf Beals, page 27 \#1:}
By the monotone convergence theorem, we have
$$
\infty > \lim \int f_n = \int \lim f_n = \int f.
$$
So by the proposition on page 27, it follows that $f$ is finite a.e.
\qed
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