---- > [!theorem] Theorem. ([[Rademacher's Theorem]]) > Let $\Omega \subset \mathbb{R}^{n}$ be an open subset. If $f:\Omega \to \mathbb{R}^{n}$ is [[Lipschitz continuous]], then $f$ is [[derivative|differentiable]] [[almost-everywhere]] on $\Omega$: $\lambda \{ x \in \Omega : f \text{ is not differentiable at }x \}=0.$ (Here, $\lambda$ denotes [[Lebesgue measure]] on $\mathbb{R}^{n}$.) ^theorem > [!proof]- Proof. ([[Rademacher's Theorem]]) > Omitted in our course. ---- #### ----- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```