Generalization of the Kozlov–Poincaré diffusion theorem for the collisionless continuous medium

In this work the generalization of the Kozlov-Poincaré diffusion theorem on weak convergence of the collisionless Liouville equation to the equilibrium distribution, which is homogeneous with respect to spatial coordinates. For this purpose the principal of measure projection in the system phase state is introduced. In these terms the theorem of existence of weak limit of distributions of Liouville equation is proved in new functional spaces.