  We discuss an equilibrium mean-field properties of mixtures consisting of
bosons and spin-polarized fermionic atoms with a point-like interaction in an
arbitrary dimension $2<d<4$. Particularly, we discuss except the standard
weak-coupling limit of the system with slightly depleted Bose condensate and
almost ideal Fermi gas, the (meta)stable phase with dimers composed exactly of
one boson and one fermion. The peculiarities of the fermion-dimer and the
boson-dimer three-body effective interactions and their impact on the
thermodynamic stability of the dilute Bose-Fermi mixtures are elucidated.
