  In order to calculate the effective mass of quasiparticles for a strongly
correlated metallic system in which the number of carriers, n, is less than
that of atoms (or lattices), l, the metallic system is averaged by one
effective charge per atom over all atomc sites. The effective charge of
carriers, <e>=(n/l)e={rho}e, and the on-site Coulomb repulsion,
U={rho}^2<e^2/r>={rho}^2kU_c, are defined and are justified by means of
measurement. {rho} is band filling and k is the correlation strength. The
effective mass, m^*/m=1/(1-k^2{rho}^4), calculated by the Gutzwiller
variational theory, is regarded as the average of the true effective mass in
the Brinkman-Rice (BR) picture and is the effect of measurement. The true
effective mass has the same value irrespective of {rho}, and is not measured
experimentally. The true correlation strength of the BR picture is evaluated as
0.90<k_{BR}<1 for Sr_{1-x}La_xTiO_3 and 0.92<k_{BR}<1 for YBCO. High-Tc
superconductivity for YBCO is attributed to the true effective mass caused by
the large k_{BR} value. The effective mass explains the metal-insulator
transition of the first order on band filling. Furthermore, the pseudogap is
predicted in this system.
