Proof of Dudley's Convex Approximation

Abstract

We provide a self contained proof of a result of Dudley [Dud64]} which shows that a bounded convex-body in ${\Re }^d$ can be $\epsilon$-approximated, by the intersection of $O_d\left({\epsilon }^{-(d-1)/2}\right)$ halfspaces, where $O_d$ hides constants that depends on $d$.

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