  The fundamental concept of phase space for particles moving in the
four-dimensional spacetime is analyzed. Particle distribution density is
defined as differential form, which degree may be different in various cases.
It should be emphasized that this approach does not include the concepts of
phase volume and distribution function. The Liouville and the Vlasov equations
are written in tensor form. The presented approach is valid in both
non-relativistic and relativistic cases. It allows using arbitrary systems of
coordinates for description of the particle distribution. In some cases, making
use of special coordinates gives possibility to construct analytical solutions.
Besides, such approach is convenient for description of degenerate
distributions, for example, of the Kapchinsky-Vladimirsky distribution, which
is well-known in the theory of charged particle beams. It can be also applied
for description of mass distributions in curved spacetime.
