Geodesic
Choice of measure and Liouville's equation in weakly relativistic statistical mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 39 (1979) no. 3, pp. 417-424

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The form of the Liouville equation depends on the choice of the measure in phase space. For the post-Newtonian approximation in statistical mechanics, classes of measures are found that are invariant along the trajectories in the phase space, and also measures that lead to probabilities invariant under a Lorentz transformation. 
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     author = {V. N. Logozinskii and I. P. Pavlotsky},
     title = {Choice of measure and {Liouville's} equation in weakly relativistic statistical mechanics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {417--424},
     publisher = {mathdoc},
     volume = {39},
     number = {3},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1979_39_3_a12/}
}
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V. N. Logozinskii; I. P. Pavlotsky. Choice of measure and Liouville's equation in weakly relativistic statistical mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 39 (1979) no. 3, pp. 417-424. http://geodesic.mathdoc.fr/item/TMF_1979_39_3_a12/