The one-particle distribution function is of importance both in non-relativ
istic and relativistic statistical physics. In the relativistic framework,
the Lorentz-invariance is possibly its most fundamental property. The prese
nt article on the subject is a contrastive one: we review, discuss critical
ly, and, when necessary, complete, the treatments found in the standard lit
erature. (C) 2001 Elsevier Science B.V. All rights reserved.