= Compact support
= Compactly supported
{synonym}
A <function> has <compact support> when its <support> is a <compact set>. On the <real line>, this means the <closure> of its nonzero region is closed and bounded. The function $f(x)=\max(0,1-|x|)$ has <compact support> $[-1,1]$.
Decay is a different condition: $g(x)=1/(1+x^2)$ tends to zero as $|x|\to\infty$, but is nonzero everywhere, so its <support> is all of $\mathbb R$ and is not compact. Smooth <functions> with <compact support> are used as <test functions> in <distribution theory>.
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