= Compact convex set
A <compact convex set> $K\subseteq\mathbb R^n$ is a <compact set> that is also a <convex set>. If $K$ is nonempty, its <support function> $H_K(\eta)=\max_{x\in K}x\cdot\eta$ is finite in every direction. For such a nonempty $K$, every exterior point $x_0$ admits a strictly <separating hyperplane>: minimize $|x_0-y|$ over $y\in K$, and put $\omega=x_0-y$. Convexity and differentiation along the segment from $y$ to any $z\in K$ give $\omega\cdot(z-y)\leq0$, while $\omega\cdot(x_0-y)=|\omega|^2>0$. This is the separation used to recover spatial support from Fourier growth.
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