  By using the Hartree-Fock-Bogoliubov equations within the Popov
approximation, we investigate the thermodynamic properties of a dilute binary
Bose-Fermi mixture confined in an isotropic harmonic trap. For mixtures with an
attractive Bose-Fermi interaction we find a sizable enhancement of the
condensate fraction and of the critical temperature of Bose-Einstein
condensation with respect to the predictions for a pure interacting Bose gas.
Conversely, the influence of the repulsive Bose-Fermi interaction is less
pronounced. The possible relevance of our results in current experiments on
trapped $^{87}{\rm Rb}-^{40}${\rm K} mixtures is discussed.
