= Convex body
A <convex body> in $\mathbb R^n$ is a <compact> <convex set> with nonempty <interior> in the ambient <Euclidean space>. It consequently has positive finite <Lebesgue measure>. A filled <rectangle> with positive side <lengths> and a closed positive-radius <Euclidean disk> are planar <convex bodies>. A <line segment> in $\mathbb R^2$ has empty ambient <interior> and is not a <convex body> under this convention. This is the convention used in the <Brunn-Minkowski theorem>. https://sites.stat.washington.edu/jaw/COURSES/520s/523/HO.523.20/Gardner.BullAMS.02.pdf[Gardner (2002), introduction]{ref}
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