Let $f_{n}(x)$ is a sequence of measurable functions on a bounded set $X$. Prove that the set $A = \{x\in X |f_{n}(x)\text{ is bounded}\}$ is measurable. I have completely run out of ideas how this can be solved.
2026-03-25 08:08:40.1774426120
Prove that the set is measurable
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Hint: $A=\bigcup_N \bigcap_{n} \{x: |f_n(x)| \leq N\}$