} = { \int _{{{{\bf}R}}^d \times {{{\bf}R}}^d}\!\!\! \psi \left (x, r { \frac{v}{|v|}}\right ) { f ^{\mathrm{in}}}(x,v)\, \mathrm{d}(x,v)}\,,$$ for all $\psi \in { C^0_c ({{{\bf}R}}^d \times {{{\bf}R}}^d)}$. 