The Spherical Hadwiger Theorem

We prove the spherical Hadwiger classification in every dimension. For $n\geq1$, every continuous $SO(n+1)$-invariant valuation on the space of all closed spherical convex sets in $\mathbb{S}^n$ can be written uniquely as a linear combination of the spherical intrinsic volumes $V_0,\ldots,V_n$. The