On kinetic interpretation of measure valued solutions to Cauchy problem for a first order quasilinear equation

In terms of a distribution function we give kinetic interpretation of a measure valued solution to Cauchy problem for a first order quasilinear equation. The known results concerning generalized solutions (in the class $L^\infty$) of the considered problem are thus generalized. Besides we describe “kinetic” solutions corresponding to strong measure valued solutions (which form a class of existence and uniqueness for original problem).