= Maximal external point
{title2=$\nexists q:\ q_i>p_i\text{ for every }i$}
= Weak Pareto maximum
{synonym}
A maximal external point of a finite set has no other point strictly larger in every coordinate. This weak nondominance differs from a <maximal element> in the <product order> when coordinate ties exist: for example $(1,0)$ passes the weak test against $(1,1)$ but is not maximal in the product order. In an independent continuous-coordinate random sample, ties have probability zero, so the two notions coincide almost surely.
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