(x,v) { \left \langle f \right \rangle }(x,v)\,{ \mathrm{d}(x,v)}\\ & = { \int _{{{{\bf}R}}^d \times {{{\bf}R}}^d}\!\!\! \psi { \left \langle f \right \rangle }}(x,v)\,{ \mathrm{d}(x,v)}- \int _{v = 0}\psi { \left \langle f \right \rangle }(x,v)\,{ \mathrm{d}(x,v)}\\ & = { \int _{{{{\bf}R}}^d \times {{{\bf}R}}^d}\!\!\! \psi { \left \langle f \right \rangle }}(x,v)\,{ \mathrm{d}(x,v)}- \int _{v = 0}\psi 