e $$\begin{aligned} { \int _{{{{\bf}R}}^d \times {{{\bf}R}}^d}\!\!\! \psi { \left \langle { \mathrm{div}_v}(fa) \right \rangle }} & = \int _{v \neq 0} { \psi \left ( x, r \frac{v}{|v|}\right )}{ \mathrm{div}_v}(fa) \\ & = { \lim _{\delta \searrow 0}}{ \int _{{{{\bf}R}}^d \times {{{\bf}R}}^d}\!\!\! \left ( 0 - { \chi \left ( \frac{|v|}{\delta}\right)}\right ) { \psi \left ( x, r \frac{v}{|v|}\right )}{ \mathrm{div}_v}(fa) 