  We describe the growth of the naturally defined argument of a bounded
analytic function in the unit disk in terms of the complete measure introduced
by A.Grishin. As a consequence, we characterize the local behavior of a
logarithm of an analytic function. We also find necessary and sufficient
conditions for closeness of $\log f(z)$, $f\in H^\infty$, and the local
concentration of the zeros of $f$.
