So this is from the book "A Probabilistic Theory of Pattern Recognition". My question is with regards to the proof of Lemma 5.5. I don't understand why we can cover the unit spheres with points that satisfy $|x_i-x_j|\geq r$. Can someone please explain to me that step. I have included pages 66-68 from the book below. Also it seems the inequality isn't even true with $d=1$.
2026-03-25 05:06:49.1774415209
Covering lemma used to prove Stone's lemma
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