 that $${ \lim _{k \to +\infty }}{ \int _{{{{\bf}R}}_+} \!\int _{{{{\bf}R}}^d \times {{{\bf}R}}^d}\!\!\!\!\!\!\varphi (t,x,v) { f ^{\varepsilon _k}}(t,x,v)\,{ \mathrm{d}(x,v)}\;\mathrm{d}t} = { \int _{{{{\bf}R}}_+} \!\int _{{{{\bf}R}}^d \times {{{\bf}R}}^d}\!\!\!\!\!\!\varphi (t,x,v) 