updates

content/Math401/Math401_P1_3.md

@@ -1,10 +1,9 @@
-# Math 401, Paper 1, Side note 3: Levy's concentration theorem
+# Math 401 Paper 1, Side note 3: Levy's concentration theorem
 
 ## Basic definitions
 
 ### Lipschitz function
 
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 #### $\eta$-Lipschitz function
 
 Let $(X,\operatorname{dist}_X)$ and $(Y,\operatorname{dist}_Y)$ be two metric spaces. A function $f:X\to Y$ is said to be $\eta$-Lipschitz if there exists a constant $L\in \mathbb{R}$ such that
@@ -17,12 +16,6 @@ for all $x,y\in X$. And $\eta=\|f\|_{\operatorname{Lip}}=\inf_{L\in \mathbb{R}}L
 
 That basically means that the function $f$ should not change the distance between any two pairs of points in $X$ by more than a factor of $L$.
 
-### Sub-Gaussian concentration
-
-### Random sampling on the $CP^n$
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-
-
 ## Levy's concentration theorem in _High-dimensional probability_ by Roman Vershynin
 
 ### Levy's concentration theorem (Vershynin's version)