 F(x,v)\,{ \mathrm{d}(x,v)}\\ & = \int _{v = 0} \psi (x,v) f(x,v)\,{ \mathrm{d}(x,v)}+ \int _{v \neq 0} \psi \left ( x, r { \frac{v}{|v|}}\right ) F(x,v)\,{ \mathrm{d}(x,v)}\\ & = \int _{v = 0} \psi (x,v) f(x,v)\,{ \mathrm{d}(x,v)}+ \int _{v \neq 0} \psi \left ( x, r { \frac{v}{|v|}}\right )f(x,v)\,{ \mathrm{d}(x,v)}