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Valuations constitute a class of functionals on convex bodies which include the Euler-characteristic, the surface area, the Lebesgue-measure, and many more classical functionals. Curvature measures may be regarded as "localised" versions of valuations which yield local information about the geometry of a body's boundary. A complete classification of continuous translation-invariant SO(n)-invariant valuations and curvature measures with values in ℝ was obtained by Hadwiger and Schneider,arXiv:1903.03100v2 fatcat:sshdluekubeg7d3fnh4cld5t64