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In traditional approach, the Vlasov equation is considered as integro-differential equation. That formulation includes partial derivatives on phase coordinates. According to the covariant approach, physical relations should be presented by tensor equations. The main feature of the covariance is that any tensor equation can be written without using of coordinates. In covariant formulation of the Vlasov equation, we use such tensor objects as Lie derivatives. Classical and relativistic cases are described similarly. A difference between these two cases appears only in form of particle motion equations. Another feature of presented approach is consideration of degenerate distributions in the phase space. By degenerate distribution we mean a distribution having support of dimension smaller than dimension of the phase space. The simplest case of degenerate distribution is the distribution described by the Dirac measure. Another example is the Kapchinsky-Vladimirsky distribution, for which particles are distributed on the 3-dimensional surface in the 4-dimensional phase space.
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