VC dimension bound for lower orthants
= VC dimension bound for lower orthants
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The class of lower orthants $\prod_{j=1}^p(-\infty,a_j]$ in $\mathbb R^p$ has VC dimension at most $p$. Among any $p+1$ points, choose a coordinate maximizer for each of the $p$ coordinates. A remaining point cannot be excluded while all those maximizers are included.