Multi-term asymptotic representations of the Riesz measure of subharmonic functions in the plane

In the paper, a multi-term asymptotic representation for distribution function of the Riesz measure of subharmonic function in the plane is considered. It is shown that the “smallness” of the reminder term of asymptotic representation does not guarantee the bounded variation with respect to the angle variable of all terms of this asymptotics, and the conditions for this property to be held are given.