  Bose-Fermion pair correlations in a mixture are considered at zero
temperature in the T-matrix approximation. Special attention is paid to the
Luttinger theorem. In a strict RPA variant of the Nozieres-Schmitt-Rink
approach, it is shown that this theorem is respected also in the homogeneous
infinite matter case. We calculate the corresponding occupation numbers of
fermions and bosons and the condensate depletion. We also show that in the
limit of very small boson density, our results are in good agreement with the
results found in the literature for the Fermi polaron in strongly imbalanced
Fermi-Fermi mixtures.
