  We evaluate the full statistics of the current via a Coulomb island that is
strongly coupled to the leads. This strong coupling weakens Coulomb
interaction. We show that in this case the effects of the interaction can be
incorporated into the renormalization of transmission eigenvalues of the
scatterers that connect the island and the leads. We evaluate the Coulomb
blockade gap in the current-voltage characteristics, the value of the gap being
exponentially suppressed as compared to the classical charging energy of the
island.
