  The hypothesis of ``molecular chaos'' is shown to fail when applied to
spatially inhomogeneous evolution of a low-density gas, because this hypothesis
is incompatible with reduction of interactions of gas particles to
``collisions''. The failure of molecular chaos means existence of statistical
correlations between colliding and closely spaced particles in configuration
space. If this fact is taken into account, then in the collisional
approximation (in the kinetic stage of gas evolution) in the limit of
infinitely small gas parameter the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY)
hierarchy of equations yields an autonomous system of kinetic equations for the
many-particle distribution functions of closely spaced particles. This system
of equations can produce the Boltzmann equation only in the homogeneous case.
It is used to analyze statistical properties of Brownian motion of a test gas
particle. The analysis shows that there exist fluctuations with a 1/f spectrum
in the diffusivity and mobility of any particle. The physical cause of these
fluctuations is randomness of distribution of particles' encounters over the
impact parameter values and, consequently, randomness of the rate and
efficiency of collisions.
  In essence, this is {\bf reprint} of the like author's paper published in
Russian in [ Zh. Eksp. Teor. Fiz. {\bf 94} (12), 140-156 (Dec. 1988)] and
translated into English in [ Sov. Phys. JETP {\bf 67} (12), 469-2477 (Dec.
1988)] twenty years ago but seemingly still unknown to those to whom it might
be very useful. The footnotes contain presently added comments.
