Quartz sync: Mar 13, 2025, 2:09 PM

content/Lectures/Lecture 17 - Lp Spaces.md

@@ -47,7 +47,7 @@ Let $p \in [1, \infty \rangle$. By [[Minkowski's Inequality]] the set of [[Measu
 > $$\| f \|_{p} = \left( \int \mid f \mid^{p} \, d\mu  \right)^{\frac{1}{p}}$$
 > $$\| f + g \|_{p} \leq \| f \|_{p} + \| g \|_{p}$$
 
-We have almost a [[Norm|norm]] $\| \cdot \|_{p}$ on $V$, except $\| f \|_{p} = 0 \centernot\implies f = 0$ almost everywhere.
+We have almost a [[Norm|norm]] $\| \cdot \|_{p}$ on $V$, except $\| f \|_{p} = 0 \;\not\!\!\!\implies f = 0$ almost everywhere.
 
 In fact $f = 0$ **almost everywhere**, in that $\exists$[[Measure|measure]] $A \subset X$ such that $f\restriction_{A} = 0$ and $\mu(A^{\complement})= 0$.