Given the hyperbolic Vlasov equation $$ \frac{\partial f }{\partial t} +v\nabla_x f + F(t,x)\nabla_vf =0$$ where $f=f(t,x,v)$ and $(t,x,v)\in \mathbb{ R}\times\mathbb{R}^{n}\times \mathbb{R}^{n} $. I wonder how can be proved that $$ \Vert f(t,x,v)\Vert_{L^p(\mathbb{R}^{2n})} = \Vert f(0,x,v)\Vert_{L^p(\mathbb{R}^{2n})}, \quad p\in [1,\infty] $$ Any hint is welcome. Thank in advance.