Stationary density distributions in the T-space

Stationary density distributions in the Tspace.a Let us assume that at time t0 we distribute an infinite number of (3-points over the unlimited r-space in such a way that by assigning a suitable measure we can define a certain spatial density p0 for each point in the T-space.84 If we select the function p0(g, p) quite arbitrarily at time U, then in general in the subsequent streaming of the G-points, the density in each point of r-space will change in time.85 

The distribution of the spatial density p will be stationary with respect to the streaming described by Eq. (22) if, and only if, p0(q, p) is chosen to be constant along each single G-path. (For different G-paths we may arbitrarily choose different values of po(q, p).) This means that p0(g, p) should have the form 

Similarly, one can use the surface density r0(g, p) to describe the distribution of an infinite set of G-points on the (2rJV—l)-dimensional hypersurface E(q, p)—ci. The necessary and sufficient condition for the stationary behavior of such a surface density a is given by87 

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