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dohmatob
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The $\epsilon$-covering number of the euclidean unit ball in $\mathbb R^d$ scales like $(1/\epsilon)^d$. More formally,

Lemma. $(1/\epsilon)^d \le N(\epsilon, B_2) \le (3/\epsilon)^d$.

Proof. See Theorem 4.2 and Example 14.1 of this manuscript http://www.stat.yale.edu/~yw562/teaching/598/lec14.pdf. $\quad\quad\Box$

Now, use this to get (an estimate of) the covering number of $rB_2$, for any $r \ge 0$.

dohmatob
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