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Zheyuan Wu
2025-04-23 10:54:34 -05:00
parent bb21338ccc
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4 changed files with 143 additions and 5 deletions
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pages/Math4121/Math4121_L37.md
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### Density of continuous functions
#### Lemma:
#### Lemma for density of continuous functions
Let $K\subseteq U$ be bounded sets in $\mathbb{R}$, $K$ is closed and $U$ is open. Then there is a continuous function $g$ such that $\chi_K\leq g\leq \chi_U$.
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If we can control all the averages, we can control the function.