  We completely classify all measurable $\operatorname{SL}(n)$-covariant
symmetric tensor valuations on convex polytopes containing the origin in their
interiors. It is shown that essentially the only examples of such valuations
are the moment tensor and a tensor derived from $L_p$ surface area measures.
This generalizes and unifies earlier results for the scalar, vector and matrix
valued case.

Metric Geometry