}} \\ & = - { \lim _{\delta \searrow 0}}{ \int _{{{{\bf}R}}^d \times {{{\bf}R}}^d}\!\!\! v \cdot \nabla _x \psi { \chi \left ( \frac{|v|}{\delta}\right)}f} - { \lim _{\delta \searrow 0}}{ \int _{{{{\bf}R}}^d \times {{{\bf}R}}^d}\!\!\! v \cdot \nabla _x { \psi \left ( x, r \frac{v}{|v|}\right )}\left ( 0 - { \chi \left ( \frac{|v|}{\delta}\right)}\right ) 