  We study the effect of electron-electron (e-e) interactions on
compressibility, capacitance and inverse compressibility of electrons in a
quantum dot or a small metallic grain. The calculation is performed in the
random-phase approximation. As expected, the ensemble-averaged compressibility
and capacitance decreases as a function of the interaction strength, while the
mean inverse compressibility increases. Fluctuations of the compressibility are
found to be strongly suppressed by the e-e interactions. Fluctuations of the
capacitance and inverse compressibility also turn out to be much smaller than
their averages. The analytical calculations are compared with the results of a
numerical calculation for the inverse compressibility of a disordered
tight-binding model. Excellent agreement for weak interaction values is found.
Implications for the interpretation of current experimental data are discussed.
