Corrections toρDominance and Pole Dominance of the Divergence of the Axial-Vector Current

A superconvergence assumption about the matrix elements allows us to discuss corrections to one-meson dominance of a current or its divergence. The deviation of the observed $\rho$ leptonic branching ratio from the $\rho$-dominance prediction and the correction to the Goldberger-Treiman relation are evaluated, and other predictions of the model are discussed.